Pollard now has 15 T20 titles, five of which has come for him while playing for Mumbai Indians. Bravo, on the other hand, has 14.
The defending champions carried out a clinical decimation of Delhi Capitals by 57 runs in the first Qualifier.
CSK are all but out of reckoning for the play-offs with just six points from 11 games, while MI jumped to the top spot with 14 points from 10 matches.
The failure of sides like KXIP and CSK so far in IPL 2020 can be attributed to the failure of the batsmen after the top three to come good on a consistent basis.
Chris Jordan was handed over the responsibility of bowling the second Super Over. The England all-rounder gave away 11 runs. The Kings XI pair of Chris Gayle and Mayank Agarwal took them home with two balls to spare.
After skipper Rohit Sharma laid the foundation with a 45-ball 70, the duo of Pollard and Pandya smashed fours and sixes at will, lifting MI to 191/4 from 83/3 in the 14th over.
Rohit Sharma's 54-ball 80 powered Mumbai Indians to 195/5. KKR could manage only 146/9 in reply.
Pollard led Trinbago Knight Riders to triumph in the CPL on Thursday.
Kohli, who was dismissed for a first-ball duck, was very animated after Pollard's first-ball dismissal in the second ODI.
The West Indies all-rounder has reversed his international retirement by making himself available for T20 selection.