India, who piled up 326-0 on the first day after being given first strike in good batting conditions, moved to 528-3 by tea on the second day at the Sher-e-Bangla National Stadium.
Tendulkar was unbeaten on 101 at the break, joining Wasim Jaffer (138), Dinesh Karthick (129) and captain Rahul Dravid (129) as the tourists' centurions in the game.
It was Tendulkar's second hundred in the series following his 101 in the drawn first Test and extended his world record tally to 37 centuries.
The 34-year-old veteran has so far batted for five hours in stifling conditions, hitting only six boundaries and a six.
Mahendra Dhoni was unbeaten on one as India looked to declare in the final session to put pressure on the Bangladeshi batsmen over the remaining three days.
Dravid, who started the second day on 88, reached three-figures within the first 25 minutes of play.
Dravid hit 15 boundaries and a six in his 24th Test hundred before he cut left-arm spinner Mohammad Rafique to Javed Omar at point 30 minutes before lunch.
It was Bangladesh's first success in the match after 108.2 overs in energy-sapping hot and humid weather.
On Friday, Wasim Jaffar and Karthick put on 175 for the first wicket before both batsmen retired hurt with severe cramps and dehydration.
Karthick, who returned to bat at the fall of Dravid's wicket, reached his maiden Test century off the last ball before lunch.
The Tamil Nadu youngster, who turns 22 on June 1 and is playing his 13th match, finally fell midway through the afternoon session when he skied a pull off seamer Mashrafe Mortaza to mid-wicket.
Sourav Ganguly, who hit a century in the previous match, was the only batsman to fall cheaply when he was caught behind off Rafique for 15.
Bangladesh coach Dav Whatmore, who ends his four-year tenure after the match, admitted on Friday that the hosts had erred in choosing to field first.
"We misread the wicket," said Whatmore. "We were taken in by the overcast conditions and believed the track would do a lot more and fetch us some quick wickets."
The first Test in Chittagong ended in a draw earlier this week after 15 of the scheduled 30 hours of play were lost due to bad weather.
Note: Mortaza went off the field after bowling four balls of his 10th over and Rasel completed the over. Rasel also went off after two balls of his 14th over and Sharif completed the over.
Brief Scores (at tea, D-2):
India 528 for 3 (Wasim Jaffer 138 retd hurt, Karthick 129, Dravid 129, Tendulkar 101 n o; Rafique 2 for 156, Mortaza 1 for 86) Vs Bangladesh.