Tendulkar – playing his 200th and final Test in his home city – looked assured during his 73-ball stay at the crease, hitting six boundaries in an typically commanding display on day one of the match.
He and Cheteshwar Pujara (34 not out) will resume on Friday, with the 40-year-old looking well-placed to score his 52nd Test century in what may be his final innings.
Earlier, the tourists lost their last seven wickets for just 42 runs in less than 15 overs to post a miserly first-innings score.
Spinners Pragyan Ojha (5-40 off 11.2 overs) and Ravichandran Ashwin (3-45 off 15) did the majority of the damage for India, who are already in firm control.
India captain MS Dhoni was unpopular at the Wankhede Stadium when he won the toss and elected to bowl, but the large crowd still got the chance to see their hero bat.
Mohammed Shami (1-36 off 12) took a nine-wicket haul on debut in the first Test and kept up his good form with the prized scalp of Chris Gayle (11) in the sixth over.
A 61-run partnership between Kieran Powell (48) and Darren Bravo (29) followed, but the loss of the latter, on the stroke of the lunch break, stemmed the momentum of the visitors.
Bravo edged Ashwin to wicket-keeper Dhoni and just after lunch, Powell fell to Ojha.
Marlon Samuels (19) faced 59 balls in a stubborn display but was also dismissed by Ojha, while Bhuvneshwar Kumar (1-45 off 17) ended the innings of Shivnarine Chanderpaul (25).
Narsingh Deonarine (21) also fell and that triggered a collapse as the West Indies tail failed miserably, with Darren Sammy, Shane Shillingford and Tino Best all dismissed for ducks.
Shannon Gabriel (one) was the last to fall, handing Ojha his fifth wicket, and Murali Vijay (43) and Shikhar Dhawan (33) saw India make a terrific start.
They scored at almost a run-a-ball through their 77-run partnership before Shillingford (2-46 off 12) removed them both in the 14th over.
Tendulkar, whose arrival at the crease and every subsequent shot was loudly applauded, steadied the ship along with Pujara, and the former's presence at the crease is sure to be the focus of attention when play resumes on Friday.