A gem from Shinja Kagawa and an unusual goal from Matthias Ginter put Dortmund ahead twice but the hosts hit back through Leroy Sane and a Klaas-Jan Huntelaar penalty.
With only five matches to play, Bayern are closing in on a fourth successive title after their 3-1 win at VfB Stuttgart on Saturday.
Schalke, who restored some pride after the previous weekend's 3-0 defeat at Ingolstadt, are seventh with 45 points, behind Borussia Moenchengladbach and Mainz 05 on goal difference.
However, their chances of qualifying for the Champions League were dented when Bayer Leverkusen won 2-0 at Cologne to go three points ahead of them in fourth, which earns a place in the playoff rounds.
"It is a very realistic scenario that Bayern will become champions. I don't know if the big comeback is really still on," Tuchel told Sky Sport Deutschland in a matter-of-fact tone.
"Of course, we were playing our 48th competitive match of the season and we are close to our physical limit."
Tuchel made eight changes to the line-up that drew 1-1 with Liverpool in the Europa League on Thursday as he rotated his side.
There was little excitement in the first half but the game sprang into life after the break.
Dortmund struck first in the 49th minute when Moritz Leitner backheeled the ball into the path of Kagawa and the Japanese midfielder dinked the ball over Ralf Faehrmann from the edge of the area.
Sane levelled two minutes later, firing home the rebound after Roman Buerki parried the ball invitingly into his path, but the game quickly took another twist.
Henrik Mkhitaryan's free kick hit a Schalke defender and looped into the area, the home defence was wrong-footed and Ginter, in between two defenders, was left unchallenged to head in the ball.
Huntelaar levelled again when the Dutchman won and converted a penalty in the 65th minute after he was shoved over by Sokratis Papastathopoulos. Both teams then had chances to win the game in a frantic finale.
"We were twice in the lead and gave the goals away a little too easily, then we had three chances to win the game, but I have no complaints," said Tuchel.
Julian Brandt and Javier Hernandez scored in a five-minute spell just before halftime for Leverkusen at neighbours Cologne, and there was a stormy end as Leonardo Bittencourt for the hosts and Wendell for the visitors were both sent off in stoppage time.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar and Clare Fallon)
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