The victory means the Knight Riders join the Delhi Daredevils as the only two teams that are through to the playoffs and, defending just 141, it was thanks to the brilliant efforts of their bowlers in making the ball talk on a helpful surface.
Narine led the way with four for 15 in 3.1 overs and the West Indian is so mysterious that, in a bygone age, his dominance would have been churlishly attributed to ball-tampering, throwing or some other dark art.
With a required run-rate of just 7.05 runs per over, Mumbai were obvious favourites as the experienced duo of Sachin Tendulkar and Herschelle Gibbs strode out to begin the run-chase.
But the tight bowling of seamer Lakshmipathy Balaji up front and the spin trio of Shakib al-Hasan, Narine and Iqbal Abdulla, the latter snaring the wicket of Gibbs, trapped lbw for 13, saw the required rate jump to over eight an over after just a handful of overs.
Tendulkar was happy to just accumulate ones and twos until the ninth over, when he punished Jacques Kallis for a six and a four.
But the glory of dismissing and thoroughly baffling Tendulkar went to Narine as he bowled him for 27 at the end of the 11th over, a fizzing off-break seemingly taking a bit of hand, bat and thigh on its way on to the stumps.
From then on it was like David’s battle against Goliath – except the underdogs didn’t get the divine intervention they needed – as Mumbai required 81 runs off the last nine overs.
Dinesh Karthik scored 21 off 26 balls before his pull shot off Balaji was perfectly placed for Yusuf Pathan to take the catch on the fine leg boundary.
Ambati Rayudu hit left-arm spinner Abdulla out of the park in the 14th over but was then stumped by Brendon McCullum for 11 when he tried to repeat the stroke against the other left-arm spinner in the Kolkata line-up, Bangladesh star Shakib al-Hasan.
Kallis then went to town in the 17th over, proving his all-round worth after a first-ball duck with the bat as he deceived Kieron Pollard (8) with a slower bouncer and then trapped Dwayne Smith lbw with the next delivery for a Caribbean double.
Any semblance of hope then disappeared for Mumbai as Harbhajan Singh, not knowing if Narine’s delivery was spinning in or turning away from him, skied a big hit to long-on.
Narine then spun out Rohit Sharma for 12, McCullum bounding out from behind the stumps to take the catch, and the 23-year-old then wrapped up the win by dismissing Rudra Pratap Singh for three with the first ball of the 20th over, earning himself the Purple Cap in the process.
The Kolkata bowlers would obviously like to put the Mumbai pitch in a box and carry it around India with them because they all thrived.
Apart from Narine, Balaji ended with terrific figures of two for 11 in four overs, Shakib produced a fine performance with one for 25, Abdulla showed his talent with one for 23 and Kallis did the wicket-taking job required of him with two for 32.
The Kolkata Knight Riders had earlier left their supporters cursing what seemed to be a mediocre batting performance as they struggled to 140 for seven.
Many tomes have been written about Kallis, but he was one of the Knight Riders batsmen to fail as he was bowled through the gate by Rudra for a first-ball duck.
In the South African’s defence, however, he errs so seldom and it was a cracking delivery from the left-arm seamer that nipped back off the seam, against the natural angle across the right-hander.
It was a disastrous start for Kolkata after Mumbai captain Harbhajan seemingly made the right decision at the toss and sent them in, McCullum having suffered an awful lbw decision from Subroto Das off the previous delivery from Rudra.
McCullum was well down the pitch, the ball pitched outside leg stump and probably would have gone over or outside off stump, but Subroto sent him on his way for a single.
Captain Gautam Gambhir (27) and Manoj Tiwary (41) brought some respite with a third-wicket stand of 38 in seven overs, but the accurate Mumbai seamers allowed them little leeway.
The Knight Riders had limped to 54 for three at the halfway mark, which finally brought out the strokemaker in Tiwary as he hit two fours and two sixes before falling to the superb Munaf Patel in the 15th over.
The lower-order did come to the party, with Shakib (13), Yusuf Pathan (21*) and Rajat Bhatia (12) all upping the run-rate, while Narine hit two fours off the first four balls he faced at the death.
The Mumbai bowlers held sway, however, with Munaf the best of the bunch with the brilliant figures of one for 17 in four overs.
Rudra finished with two for 33, while Lasith Malinga was unusually in the background as he took one for 32. The medium-pace of the West Indian duo of Pollard (3-0-20-1) and Smith (2-0-8-1) was also impressive on the helpful Wankhede pitch.