In a shootout for the final place in the top three, Sutherland's unbeaten 62 off 36 balls helped Leeds win by 41 runs at Old Trafford, leapfrog their opponents and set up an eliminator against Southern Brave.
That means Sunrisers' Aussie cohort of Sutherland, Phoebe Litchfield and Jess Jonassen will come up against compatriot Sophie Molineux, the Braves captain who is expected to have recovered from the upset stomach that ruled her out of Monday's defeat by Trent Rockets.
Opener Litchfield made her intentions clear after Sunrisers were asked to bat, dashing to 27 from 12 deliveries to leapfrog Trent Rockets' England batter Sophia Dunkley at the top of the competition's run-scoring chart.
All-rounder Sutherland hit nine boundaries, including three sixes, as the visitors posted 4-166.
Sutherland told Sky Sports: "It's the beauty of being an all-rounder, you're in the game all the time, and I love competing, especially in a match we were calling a final. We had to win and it was nice to do a job for the team."
Jonassen utilised her spin to take 3-21, while Deepti Sharma and Sutherland claimed two wickets apiece as Manchester, for whom their Aussie captain Meg Lanning made 10, were restricted to 8-125 in reply.
They exit the competition after slipping to fourth place in the standings.
Second-placed Leeds will continue their title defence against Southern Brave on Friday at the Oval, with table-topping Trent Rockets, captained by Aussie Ash Gardner, awaiting the winners in Sunday's final at Lord's.
