The Sri Lankan veteran flicked, slashed and pulled the short-pitched balls served to him on a platter by the visiting team's bowlers as the home team, chasing Chennai's total of 156 for six, surged to a comprehensive win in only the 14th over.
Jayasuriya finished the match with a flourish by slamming Lankan compatriot Chamara Kapugedara for 26 runs in five balls, with three sixes to boot.
It was the 'Marauder from Matara' who stole the honours of the day with clean hitting as he took the match away in the first six overs when 78 runs were made, mainly through his efforts.
He raced away to his fifty in 25 balls and his hundred came off just 45 balls, studded with seven fours and 10 sixes.
Jayasuriya and fit-again Mumbai Indians skipper Sachin Tendulkar, who made 12 in 16 balls with a six and a four, put on 82 for the first wicket in only 44 balls to consign the visitors to a comprehensive defeat, their fourth in 10 games.
The Lankan lost Tendulkar in the eighth over, bowled through the gate by Joginder Sharma when the champion batsman tried to play an on-drive, but carried on relentlessly to ensure that his side came out victorious.
Chennai new-ball bowlers Manpreet Singh Gony and South African Albie Morkel erred in trying to bounce out the great left-hander on a helpful pitch but just did not possess the much-needed accuracy and went for plenty.
Gony went for 31 in his first three overs, while Morkel conceded a whopping 44 from the same number of overs. Jayasuriya struck three sixes each in one over off either pacers.
The Lankan ace's initial pyrotechnics sealed Chennai's fate much before the end came.
Earlier, Subramaniam Badrinath and Mahendra Singh Dhoni revived the visitors with a 95-run stand after the hosts' pace attack had taken early control.
Badrinath, struggling initially before picking up pace, struck his second successive half century in the IPL when he made 53 off 32 balls with seven fours and two sixes, while his skipper Dhoni made an unbeaten 43 in 35 balls with six fours and a six as the fifth wicket pair pulled Chennai out of the hole with their 95-run stand in 61 balls.
The recovery came after the Mumbai Indians pace attack put them on the rack to leave them gasping at 46 four in the ninth over.
Put in to bat, Chennai began well by hitting a string of boundaries in the second over before they were rocked by the Mumbai attack and pushed on the back foot.
In the top-order, Stephen Fleming (26), dropped on one, and fellow-opener Vidyut Sivaramakrishnan (16), who was the first to go, got a start but failed to build on it.
Suresh Raina made only one run before edging a rising ball from Dwayne Bravo to 'keeper Yogesh Takawale to leave Chennai at 28 for two in the sixth over.
Then two wickets fell in one over of Dhawal Kulkarni, both with the total reading 46: those of Fleming, who faced 29 balls and played the cut shot well to hit four fours, and man-in-hurry Chamara Kapugedara (1 in 2 balls).
Fleming, after striking the young medium pacer for a four to square point, dragged the next ball on to his stumps when playing well away from his body.
Sri Lankan Kapugedara fell for nought, edging a rising ball from Kulkarni that left him off the pitch to stumper Takawale.
Pollock then came back for his fourth and final over, a maiden, and troubled Dhoni.
Badrinath, who played some audacious scoop shots to fine leg, and Dhoni, who hooked Rohan Raje for the first six of the innings in the 18th over, took the score past the 100-mark in the 16th over.
The last five overs fetched 67 runs for the visiting team as the pace bowlers, after Pollock had finished his quota, were punished at will.
However, the Chennai Kings' total proved inadequate against Mumbai Indians' strong batting line-up led by the rampaging Jayasuriya at his destructive best.