In pursuit of 148 for a sixth win in seven matches, the Rockets made a shaky start, losing Finn Allen, Aneurin Donald, Sam Billings and Ben Duckett with just 70 runs on the board halfway through their innings at The Oval in London on Saturday (local time).
But an unbeaten 32 off 24 deliveries from David - crowned Australia's best T20 player last week - and a brilliant 52 not out off 23 balls from No.6 Santner catapulted the Rockets to victory with 10 balls in hand.
The Rockets extended their lead at the top of the table to eight points and hold the same advantage with a better net run-rate over fourth-placed Welsh Fire, who have two games to play.
MI London lost opener James Vince and Nicholas Pooran in quick succession, and after Will Jacks departed for a quickfire 39 the home side were indebted to Sam Curran, who hammered five sixes and four fours in a 46-ball 72, but it was not enough.
Manchester Super Giants boosted their bid for a top-three finish with a 10-run victory over Southern Brave at Southampton.
The Super Giants built their score of 8-149 around an opening partnership of 119 between Tim Seifert and Paul Walter.
Seifert made 55 from 34 deliveries before being run out by Moeen Ali, while Walter hit six fours and four sixes in his 32-ball 64.
Wickets tumbled at the end of the innings, with Adil Rashid picking up 2-17, but the target was just beyond Brave, whose Eliminator hopes are now over.
Tristan Stubbs led the reply with an unbeaten 53 from 28 deliveries, and Jamie Smith and Australia's Marcus Stoinis chipped in with 26 and 21 respectively.
A 19-ball 10 from Nikhil Chaudhary, who made his T20 debut for Australia in June, gave Brave hope, but Gus Atkinson produced brilliant bowling at the death to lift the Super Giants into the top three on run rate.
- with PA
