The wicket of Tendulkar, who struck 11 fours and a six in his excellent innings, triggered the collapse as seven wickets fell for just 15 runs which almost put Mumbai on the brink of defeat.
West Indian Smith pulled it around with his splendid, unbeaten 24 in 9 balls, that included 2 sixes and as many fours.
Tendulkar and Rohit's partnership had virtually looked to have sealed Chennai's fate on a splendid batting track before the sensational collapse.
The duo had cut to size the Chennai attack that looked clueless on how to stop the rampaging second wicket pair. Rohit hit eight boundaries, including two sixes.
Tendulkar departed in the 16th over, caught brilliantly at short extra cover by Francois du Plessis off R Ashwin when 30 runs were needed and what appeared to be a comfortable task became difficult with a spate of wickets including that of Rohit in the 18th over.
The mayhem began when Dwayne Bravo castled Dinesh karthik (11) and Ravindra Jadeja struck twice in the 18th over to remove Ambati Rayudu (0) and Rohit.
In the end their third straight victory boosted Mumbai's tally to 14 and placed them one point adrift of second-placed Kolkata Knight Riders.
In Image: Mumbai Indians' Dwayne Smith celebrates their win against Chennai Super Kings