Set a target of 197 in 38 overs by the visitors, the hosts won on a canter after a solid start from openers Sahil Kukreja (80 not out) and Vinayak Samant (67).
The Mumbai openers put on 129 runs in only 26 overs to give the home team a flying start in their run-chase and then Pakistan-bound Wasim Jaffer showed splendid touch with a smashing innings of 44 not out in 19 balls.
Jaffer, chosen as one of the three openers for the upcoming three-Test series, clouted spinner S Badrinath for 24 runs in one over with three fours and two sixes.
Badri had replaced off-spinner Ashish Kapoor after the latter was carted around for 16 runs in his over, ten of them by Jaffer, which included a six. In all, the batsman played for 25 minutes and clubbed three sixes and five fours.
Kukreja played for 141 minutes and struck six fours and with Samant, who hit six fours in 84 balls before being trapped leg before by Kapoor, gave the chase the right impetus.
Earlier, S Badrinath (64), captain Hemang Badani (48), Sridharan Sharath (59) and Naresh (58) kept Tamil Nadu in with a chance to force at least a draw. But Sharath's dismissal at 318 opened the door for Mumbai's victory.