Jayasuriya returned with 3-14 and Pollock 2-27, but the home side got a semblance of respectability through Laxmi Ratan Shukla (40) and Debabrata Saha (29), which gave the Kolkata side some glimpses of hope from a hopeless situation earlier in the match.
Jayasuriya had David Hussey and Ajit Agarkar caught by Ashish Nehra at long-on in identical fashion. Between those two dismissals, he also removed Mohammad Hafeez while Ponting was run out as Kolkata slipped from 74-3 in the 12th over to 77-6 in the 14th and then to 90-7 by the 16th over.
Shukla then produced a blitzkrieg in which he dispatched the ball to all parts of the ground, much to the excitement of a packed house.
Earlier, Pollock, leading the team since Harbhajan Singh's ouster from the tournament because of a ban, produced an inspired opening over in which he dismissed openers Brendon McCullum and Sourav Ganguly.
Pollock had Ganguly caught by Sanath Jayasuriya at wide slip immediately after the left-hander had dispatched a delivery from the South African to the mid-wicket boundary with a short-arm pull.
Pollock then trapped McCullum leg-before as he shuffled across.
Debabrata Das was the third batsman to be dismissed, his flurry of shots on the leg side getting him 29 off 19, but a slash outside off giving Dwayne Bravo a wicket in his first over. Robin Uthappa, fielding at point, accepted the catch gleefully.
Mumbai Indians went without their captain Sachin Tendulkar and banned Harbhajan Singh. The team tasted defeat in all the four matches, while the Kolkata team romped home in two and lost to Chennai Super Kings in the last outing.