Lou Vincent got Auckland's chase off to a fine start with 30 from just 12 balls while Black Caps opener Martin Guptill added 25 from 26 balls. Anaru Kitchen chipped in with 24 from 15 balls.
The Aces chased down Kolkata's tally with 14 balls to spare.
Auckland skipper Gareth Hopkins told Star Sports that the side didn't panic after the Knight Riders got off to a solid start at 61 for one after eight overs. Nine balls later they were 72 for four.
"I think once they got off to such a good start we didn't worry. We got those wickets and we kept going and I think that helped with the run chase.
"Lou got us off to a good start, got the momentum and left it up to the master Mahmood to take responsibility and finish it off, as he does."
Auckland's next match is against South African side the Titans on Thursday. The Titans won their opening match against the Perth Scorchers on Sunday.
Today's defeat is the second for the Knight Riders after a heavy 52 run loss to fellow IPL side the Delhi Daredevils.
- nzherald.co.nz