Raina was out in the 12th over to end his 145-run partnership with Rayudu. Harbhajan then applied closure to the innings with Rayudu, who faced 289 balls, and Wridhiman Saha (20) at the crease, 52 minutes before lunch.
Chasing the improbable target, Mumbai lost the wickets of opener Aditya Tare (11), Ajinkya Rahane (25), Rohit Sharma, who flopped for the second time in the match by scoring one after his duck in the first innings, and captain Abhishek Nayar (2).
Jaffer and Rahane, who made 80 and 83 respectively in the first innings, put on 53 runs in 85 balls for the second wicket before the latter was sent back by Harbhajan.
Tare, dropped by Rayudu at long on off Harbajan, fell to the rival captain two runs later, caught in the leg trap and the off-spinner, selected in the Indian squad for the first two Tests against Australia, sent back Rahane in a similar fashion to show encouraging return to wicket taking ways ahead of the four-match series.
Jaffer batted for 200 minutes and struck ten fours in his 141-ball knock and also crossed the 1,000-run mark to become the highest scorer in the tournament�s history to remain unbeaten along with Ankit Chavan (12) when stumps were drawn for the last time.
Harbhajan picked up 2 for 38 while Pragyan Ojha dismissed Rohit by having the batsman, who again had a rush of blood early in his innings like in the first, through a catch at mid off and finished with 1 for 45. Raina accounted for Nayar.