Openers Rahul Tripathi (45) and Ajinkya Rahane (38) added 76 runs for the first wicket, the franchise's best of the season so far, after the home team opted to bowl at the Wankhede Stadium.
Skipper Steve Smith and season's highest signing Ben Stokes fell for an identical score of 17, before Manoj Tiwary blazed away to 22 off 13 balls to help the visiting side reach a modest total.
Meanwhile, veteran off-spinner Harbhajan Singh got to his 200th Twenty20 wicket when he dismissed Smith in the 13th over.