The visitors then lost Herchelle Gibbs for two after KP Appanna fired in a superb throw at the bowler's end where Tiwary did the rest.
MI were in trouble with the scorecard reading seven for two at the end of the second over.
Mumbai wicketkeeper batsman Dinesh Karthik showed early signs of aggression as he carted Zaheer over backward square leg for a boundary and then worked him between the midwicket and mid on for another four.
Rohit Sharma's dismissal only made things worse for MI.
After the end of seventh over, Mumbai needed 132 runs off 78 balls at 10.15 per over.
In Image: Mumbai Indians player Sachin Tendulkar returns to the pavilion after his dismissal