Stubbs was the standout South African performer, striking 38 off 31 balls to help Southern Brave to 129-9.
David Miller chipped in with 8, while South African-born Tom Curran, playing for MI London, was bowled by Nikhil Chaudhary for 7 during a dramatic run chase.
MI London eventually got home from the final ball, with Ollie Pope sealing a three-wicket win. Will Jacks top-scored for the visitors with 54, while Marcus Stoinis starred with the ball for Brave, taking two wickets in two balls during the powerplay before returning to finish with 3-17.
The chase went down to the wire, with Sherfane Rutherford’s late hitting for MI London countered by a string of run-outs, before Trent Boult and Pope combined to see their side home with three needed off the final three balls.
The result took MI London up to third in the table, while it was a third consecutive loss for Southern Brave.
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