The South African duo forged a quickfire 55-run stand as Challengers overhauled Indians' total of 165 in the final over.
Boucher remained unconquered on 19-ball 39 and Kallis made a run-a-ball 28. Skipper Dravid made a workmanlike 32 while Ross Taylor and Virat Kohli chipped in with brisk 23 apiece.
Pollock bowled a tidy spell as often he did but his hardwork was undone by Nehra, who conceded 18 runs in the penultimate over of the Mumbai Innings, went for as many as 45 in his four overs.
Challengers had a perfect game plan with Dravid and Kallis playing the anchor role while the others took to the attack.
Challengers chasing a stiff target got off to a fine start with Chanderpaul and Dravid targetting Nehra for some severe punishments. The right-hand left-hand duo took as many as 21 runs off Nehra's first over.
Chanderpaul, who played a crucial role in Windies' series win against Lanka last week, was timing the ball well before he took a nasty blow that halted his flow and his stay at the wicket flicking the same bowler straight to Nayar at long-leg.
The next man in Ross Taylor gave solidity to the chase with a quick 23. Ross a attacking batsman by instinct is Taylor-made for this format. The Kiwi hit a four and two sixes in his 12-ball knock before trying one too many was holed out to Nayar at long-off-off Jayasuriya.
The young Kohli too played a gem of a cameo innings. He along with Kallis took Chargers past 100 in the 14th over. He top-edged a ill-timed pull off Nehra to give Indians' gloveman Ronchi a simple catch.
At the end of 16th over Bangalore was left with a big ask of scoring 40 runs with their two tried and trusted soldiers Kallis and Boucher at crease.
Boucher, who has got an uncanny habit of playing in the pressure situations, eased off the pressure on B'lore belting Nehra in the penultimate over of the innings for a massive six over long-on that flew past the ceiling of the stadium and followed it with a boundary over point.
B'lore outfit left to score just three runs in the last over did it with ease.
Earlier, Robin Uthappa's 38-ball 48 and Jayasuriya's quickfire 29 up the order and the fine rearguard action from Pollock (28 off 12) and Abishek Nayar (20 off 14) helped Mumbai Indians reach a healthy 165
Mumbai Indians, who received a blow before the match when their captain, the batting maestro Sachin Tendulkar ruled himself out of the match, still not having recovered from his groin injury, saw stand in captain Harbhajan Singh win the toss and elect to bat first.
Indians who opened with L Ronchi and Sanath Jayasuriya saw the former give them a flying start, smashing Praveen Kumar for two boundaries in the first over itself over the cover region.
However, Zaheer Khan gave the Bangalore Royal Challengers the breakthrough they wanted in his first over, when Ronchi tried to cut Zaheer, but Virat Kohli at point dived to his left to bring up a stupendous catch. Ronchi fell for 8 which came in a stay of 10 balls and was inclusive of two boundaries in it.
Mumbai Indians then suffered another blow when Dominic Thromble was hit on the face while trying to hook Zaheer Khan and had to retire hurt.
However, the marauder from Matara Jayasuriya then took to the attack hitting Kallis' first ball to the long-off fence and then on the next ball repeated the shot for the same result. Two balls later he flicked the South African for a four to fine -eg and then on the last ball send the ball soaring out of the ground, for a huge six over, deep mid-on to take 19 runs of Kallis" first over as Mumbai Indians stepped on the accelerator.
Jayasuriya (29 off 16) going for a cheeky single faied to beat the throw from Zaheer.
Robin Uthappa was then joined by Pinal Shah and the two put on 51 runs in 7.5 overs before Pinal Shah was caught by Kohli off the bowling of Balchandra Akhil for 19.
Robin Uthappa however continued on run playing some unconventional shots, before falling just two shot of his 50 being stumped by Mark Boucher of B Akhil. His 48 runs came in 38 balls and was inclusive of five fours and a six.
Final onslaught by Abhishek Nayar and Shaun Pollock saw Mumbai reach 165.