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Given a 600 character limit per post here, I'll try. Song in question:
Intro A: Ab - Bb - Ab - Bb. Suggests we'll be in Eb Major or a related key.
Intro B (with initial vocal): Ab - Bb - C minor (relative minor of Eb) x4. Expectation met. Move to verse set up with Bb. (cont'd)

Verse A (0:40): C min - Ab - C min - Ab - Bb x2. Melody centers around C and Eb, with the end of the phrases using F and G (suggesting F min - G min in first inversion at the end of the phrase).
Verse B: F min - Bb - Eb - Ab - D dim - G (major) - C (major) - F min - Bb - Eb - E dim - F min - Bb - C min
...there's a lot going on here. The circle of fifths is pretty standard, but the G major and C major introduce a new group of notes (from the C major scale) that subverts expectation. The aborted second pass through (moving up through the E dim) also truncates the expected form.

Then back to intro B, and back through the verse. After that,
Chorus: Eb - Bb - C min - Ab - Bb x2 with an Eb tag. Now we're in the relative minor, which gives a certain sense of brightness compared to everything before this.
Solo: C min - Bb - F (major)/A - Ab - Bb x2; Verse B; Chorus x4 w/ Eb tag to end.

As for the melody in the Verse B, he's mostly using the third of the chord (so an Ab over the F minor, a D over the Bb, etc.), and that follows the circle of fifths around (which includes the E natural over the C major, giving this the unexpected lift). This ends on the second Eb, where he goes to the fifth (Bb) rather than the third (G), which is immediately followed by the break from the circle with the E diminished chord, so the whole effect is to jar the listener abruptly.