Bista and Lad both hit identical scores of 123 and also featured in a fighting stand of 146 for the fifth wicket to pull Mumbai from a tricky 77 for four to 223.
Then Lad, who had saved Mumbai from a defeat in the previous home game against Baroda with an unbeaten knock of 71, and his skipper Aditya Tare (67) stitched a partnership of 97 runs for the sixth wicket to put the home side in total command on day two of the four-day match at the Wankhede Stadium.
At stumps, Dhawal Kulkarni (50) and Minad Manjrekar (8) we're at the crease.
With two days left in the match, Tripura look headed for a big defeat which is what is needed for 41-time champions Mumbai to book their berth in the quarter finals.
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The day belonged in the main to Bista, playing in only his third match of the season, and the diminutive Lad who has been very consistent and whose tally for the season has crossed the 600-run mark.
Bista, when on 75, was grassed by Yashpal Singh at first slip off left arm slow bowler Gurinder Singh with the score on 125 for four.
He finally departed after facing 136 balls and hitting 17 fours, ten minutes before lunch off medium pacer Mura Singh after completing his careers third hundred in his 12th first class match.
Bista's earlier hundred of the season came in the first game against Madhya Pradesh after which he was dropped before he regained his spot in the previous game against Andhra at Ongole.
Lad got out when the tea break was approaching, caught at deep point after facing 197 balls and striking 16 fours and 2 sixes.
It was the batsman's 6th first class hundred. His earlier ton in the season was scored against Odisha and he has three other half centuries to his credit this season.
Tare then continued to pile on the agony for the visiting team before he was dismissed after scoring his second half century of the season.
Brief scores: Tripura 195. Mumbai 421 for 8.(Jay Bista 123, Siddhesh Lad 123, Aditya Tare 67; Dhawal Kulkarni not out 50, Minad Manjrekar not out 8; Mura Singh 5 for 71).