Chasing 184 for a win after Tamil Nadu had been bowled out in 49.3 overs, Shubam Ranjane (59 not out) came to Mumbai's rescue after the team had slumped to 79 for 5.
India Test spinner Ravichandran Ashwin had brought Tamil Nadu back into the game with a tight spell, during which he scalped skipper Aditya Tare (17) and Surya Kumar Yadav (21).
Earlier, the host endured a poor start as Dhawal Kulkarni sent back opener M Kaushik Gandhi caught behind by Tare in the first over for a duck.
Ashwin (41) and N Jagadeesan (31) managed the only half-century partnership of the innings as the team struggled to 183 all out. Kulkarni was the most successful Mumbai bowler with three wickets while Ranjane and Dhrumil Matkar scalped two each.
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When Mumbai batted, they too didn't have things their way. Young sensation Prithvi Shaw, fresh from leading India to triumph in the Under-19 World Cup in New Zealand, hit two boundaries, but was sent back by K Vignesh in the third over.
The quick loss of Tare and Yadav would have raised Tamil Nadu's hopes but Ranjane followed up his spell of 2 for 28 by hammering six fours and two sixers to see Mumbai home.
In other matches, Goa picked up a second straight victory, beating Rajasthan, after having shocked Tamil Nadu on Tuesday, while Madhya Pradesh coasted to a five-wicket win over Gujarat.
Mumbai tops the group with three wins while Tamil Nadu has lost two of its three games so far.
Brief scores: Tamil Nadu 183 all out in 49.3 overs (R Ashwin 41, N Jagadeesan 31, Dhawal Kulkarni 3 for 44) lost to Mumbai 184 for 8 in 48.5 overs (Shubam Ranjane 59 not out, Shivam Dube 28, R Ashwin 3 for 35). Points: Mumbai: 4; TN: 0.
Gujarat 248 all out in 49.4 overs (Priyank K Panchal 65, Dhruv Raval 51, R H Bhatt 56, Anshul Tripathi 4 for 37) lost to Madhya Pradesh 253 for 6 in 45 overs (Harpreet Singh Bhatia 76, Rameez Khan 75, Piyush Chawla 3 for 54). Points: MP: 4; Gujarat: 0.