Chasing a mammoth 408 runs for an outright win, Baroda were bowled out for 238 in 77.3 overs in their second innings.
Coming out to bat at the overnight score of 67 for two, Baroda lost wickets at regular intervals with Thakur (5/39) doing the bulk of the damage to ensure the win for Mumbai.
Kedar Devdhar top-scored for Baroda with an unbeaten 58, while last man Munaf Patel struck a quickfire 3 off 35 balls towards the end of the innings. Opener Saurabh Wakaskar (48) and Deepak Hooda (32) were the other notable contributors for the hosts.
By virtue of this win, Mumbai will return home with six points from the match.
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Brief Scores:
Mumbai: 287 & 304/9 decl in 67 overs (Shreyas Iyer 90, Nikhil Patil 50 not out; Yusuf Pathan 5/80)
Baroda: 184 & 238 all out in 77.3 overs (Kedar Devdhar 58 not out, Munaf Patel 53; Shardul Thakur 5/39).