With this win, Mumbai take their points tally to 19, three more than second-placed Punjab and five ahead of third-placed Gujarat.
Badrinath, who began on his overnight score of 101, scored 192 before being bowled by paceman Sandeep Singh. His knock came off 381 balls with 21 fours and three sixes.
S Badrinath, who is yet to earn his place in the Indian Test team, remained unconquered on 101 off 190 balls to set the platform for a big first innings score for Tamil Nadu.
Pune Warriors may have had an off day against Mumbai Indians at the Wankhede Stadium on Wednesday, but Shrikant Wagh's parents had a field day.