Electing to bat after their captain Zaheer Khan won the toss, Mumbai were reduced to 85 for four but Jaffer held one end to steer the visiting team to 207 for five.
Jaffer's 175-ball knock was studded with 11 fours and a six. Another notable contributor to the team's cause was Suryakumar Yadav, who struck 44 off 82 deliveries.
Yadav put together 102 runs for the fifth wicket with Jaffer before falling to all-rounder Yuvraj Singh.
It was not the best of starts by Mumbai as they lost their first wicket in the form of opener and wicketkeeper Aditya Tare (11) with just 17 runs on the board.
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His partner Kaustubh Pawar (24) hung around a little longer but it was just not enough to rescue Mumbai. The fall of two quick wickets after his dismissal raised fears of a collapse but Jaffer and Yadav rebuilt the innings.
Punjab bowlers kept it tight and did not allow Mumbai batsmen to break the shackles after putting them under pressure with early dismissals.
At stumps, Hiken Shah (9) was giving company to Jaffer as Mumbai partially recovered from the morning collapse.
Brief Scores:
Mumbai 1st innings: 207/5 in 71 overs (Wasim Jaffer 92 batting, Suryakumar Yadav 44, Siddharth Kaul 2/40).