Melbourne Renegades 143 for 4 (Finch 63*) beat Adelaide Strikers 142 for 7 (Carey 65, Ahmed 3-17) by six wickets
Finch survived some early scares - including a ball hitting his stumps but failing to dislodge the bails - to hit an unbeaten 63 to guide Renegades home with 10 balls to spare at Marvel Stadium.
Australia's T20 captain notched up his fourth 50 of the tournament and 26th in the BBL, and was joined at the crease by Jon Wells to finish off the match.
Finch stayed calm as wickets fell around him, including those of former international stars Martin Guptill and Shaun Marsh, as he built his innings before powering the Renegades in the final 10 overs after they had been 16 for 3 in the third over.
After winning their first title in 2019, Renegades endured three grim seasons before putting in a much-improved campaign.
They will now have a home final after taking care of Strikers to snap a two-game losing run and will either finish third or fourth depending on Wednesday's results barring a huge net run-rate swing.
Sydney Thunder could jump above the Renegades into third if they smash Melbourne Stars at the MCG and make up the net run-rate gap while Brisbane Heat also lose.
Even Travis Head, who has become one of Test cricket's most explosive middle-order players, struggled to 19 from 32 balls.
Strikers' innings slumped to new lows when Wells ran out Cameron Boyce with a long throw from halfway to the boundary.