Written in the month of June 1865, the final movement of Brahms' e-minor sonata provides a powerful end to the entire work, strikingly different in character from the mostly calm and elegant second movement. It is written in fugal structure and contains multiple four-bar melodies that flash out of the thick texture throughout the entire movement. The first theme - characterized by two quarter notes an octave apart and followed by a series of triplet eighth notes - is introduced by the piano's left hand voice and immediately sets the movement's pace. In measure 5, it is followed by the 'cello's restatement of the same theme, though centered around the dominant, while the piano's left hand introduces the second theme, a series of 7 eight notes (all except the first one played staccato) starting on the second half of the second beat, which expands into a series of 9 such staccato notes in the fourth measure of the theme. It is interesting how the triplet eighth notes of the primary theme and the duplet eighth notes of the secondary theme are juxtaposed, a feature that reappears throughout the movement. As expected, the 'cello takes over this theme in bar 9, presenting it in the tonic. The piano's left hand meanwhile plays the third melody of the movement, which starts with an arpeggio-like figure followed by a trilled quarter note, followed in the third measure of the tune by a G - E - F# - D# melodic line in eighth-note octaves and in syncopated rhythm. It is also at this point that the right hand of the piano enters as its own independent melodic line, picking up the very first theme.

The first arrival point is reached in bar 16, at which point the first tune returns in the piano's left hand. This arrival point is introduced by a three-measure buildup consisting of repetition of bar 12, but with the distribution of the three voices (two hands of the piano and 'cello) alternating each measure. Interestingly, the left hand of the piano drops out in measure 20 after its restatement of the opening theme; instead, it takes on an accompanying role to the right hand, which in measure 20 plays the third theme. This reduction in texture is accompanied by a drop in dynamic level in both instruments. The 'cello also ceases to follow the order in which the themes were presented in the beginning; instead of returning to the first theme, it restates the second theme. This time, however, the ending expansion of the eight-note staccatos is prolonged into a series of 17 such notes, leading into another arrival point in the second half of measure 25, marked by a rhythmic relaxation in the cello in the form of a middle C quarter note followed by a C two octaves lower and 4 beats long. However, it is quickly made obvious to the listener that this place is not the final point of arrival, as the length of the two notes in the cello is constantly reduced: first, the lower note is shortened to three beats (measure 27); next, the same note is reduced again to a quarter note (measure 28, 29); finally, both notes are diminished to eighth notes (measure 30). The piano goes through similar rhythmic changes: at the same time where the 'cello is holding its first long low C, the piano plays three sets of triplet eighth notes followed by a quarter note, with the quarter note tied to the first of the eights. This pattern is reduced in measure 28 to one set of triplet notes followed by a quarter note, and again in measure 30 to only triplet quarter notes, where the first note of each triplet is the only remainder of the former quarter note. The arrival point that this section is hinting towards follows in bar 31; it is one of the two strongest arrival points in the exposition if not the strongest. Here, the 'cello, pounding in its lowest registers, restates the original theme, and adding to the intensity of this passage the piano plays the same rhythm, but offset by a beat, transposed into higher registers, and with the theme in inverted form. The same pattern is repeated in measure 35, but with the two instruments in switched roles. This climax is followed by a calmer closing theme in measures 38 - 43, which concludes in one final, but minor, arrival point in measure 42.

The development section begins with a very light mockery of the first opening theme in a major mood, although it is not entirely clear, what key it is in. This confirmation appears in measure 53 in the form of a V-I progression in the key of G major. Here, the piece calms down to its perhaps most peaceful moment of the entire movement; Brahms indicates this with the word "tranquillo" in the score. The left hand of the piano develops the second theme in the exposition by restating it in G major and articulating it in legato. The 'cello takes over in measure 55 by presenting a melodic line that on first sight seemed to me like new material; however, the three quarter notes correspond with the first three eighth notes of the second theme, thus representing an example of rhythmic augmentation. This section also contains an example of a technique typical to Brahms' compositions called "developing variation," where a melody is developed into something different every time it occurs. In this movement, this technique easily seen by comparing measures 53 - 58 to 59 - 69.

In measure 76, the development section suddenly switches into a more energetic mood; again, Brahms indicates his intent with the word "animato." The following section grows out of the first theme: the 'cello and the right hand alternate in playing triplet eighth notes, while the left hand's part reminds of the very first two notes of the piece. Again, the two instruments switch roles in measure 80. However, in measure 82, a growth in intensity is indicated by a speedup in the frequency of the notes in the 'cello, which ultimately leads into a furious descending (in thirds) scale. At the end of the scale, the piece has modulated into g minor; a dramatic 4-measure solo for the piano follows characterized by a repetition of the first opening theme in both hands but offset by two beats (measures 91 - 94). The 'cello enters again in bar 95 with a fragment of the third theme (only the first bar), a pattern which the piano imitates two beats after the 'cello's entrance. The eight bars from 91 to 98 are repeated in another instance of "developing variation" starting in measure 99; this time, the cello joins the piano after two measures, and the development of the third theme continues through 6 bars. In measure 111, the fragmentation of the third theme is further reduced to a simple eighth note followed by a dotted quarter note. This pattern is played in both the 'cello and the piano, with the piano's left hand offset by one beat, and repeated over four bars accompanied by a crescendo and ultimately leads into the climax of the development section in bar 115, an inverted restatement of the first theme in b minor in the 'cello. The piano's right hand plays the same melodic line, while the left hand plays a b pedal continuing throughout the passage. This climactic passage is repeated, and the second time, the piano's two hands switch, adding yet more intensity by having the dramatic melodic lines in both a high register ('cello) and a low register (piano's left hand). The passage comes to a sudden stop in measure 123, where in a dramatic change of mood and character the 'cello picks up the same melody as earlier in the development section in measures 55 and 63, bringing the development section to a close in measure 132.

The recapitulation starts out with a restatement of the first theme, however, it does so in the key of B major accompanied by the 'cello playing the second theme in B major as well. This is exactly the same as in measure 5, but with the 'cello and piano in reversed order. The correct distribution of voices is restored in the next section (measure 136). From here on, the recapitulation is almost identical to the exposition, until measure 169, where a low B natural and high C# (Cadential 6 4 going to vii/V in the key of e) take the place of a C natural and A natural (V42 of G major) in the exposition (actually, the first subtle differences appear several measures earlier in the piano). The next five measures serve to calm down the mood and lead into the Coda, which starts in measure 175.

The Coda returns to triplet eighth notes pattern, thus picking up the opening's energy and spirit. Most of the section consists of a series of swells until it finally reaches a giant crescendo starting in measure 185 which via a continually rising line in both the 'cello and the piano's right (while the piano's left hand travels in the opposite direction) hand reaches the climax of the Coda in measure 189. Finally, the movement comes to a furious end in a descending pattern in both the 'cello and the piano marked by Brahms as fortissimo, concluding in a powerful Neapolitan 6 - V7 - I progression in 2 beat intervals and bringing an incredible final movement of an incredible piece to an end.