No.8 Green came in with the Thunder precariously placed at 6-95, having lost 3-15 in eight balls as they pursued a DLS-adjusted target of 140 at Engie Stadium.
With all the pressure on his shoulders, Green bludgeoned three sixes in as many balls from Gurinder Sandhu (4-42), the Renegades' best bowler to that point.
It swung Monday's game dramatically back in favour of the Thunder, who would have been consigned to the wooden spoon with a loss to the Renegades.
Instead, Green (34no off 13 balls) and Nic Maddinson (30no off 17 balls) piloted Thunder to their second win of the season with an unbeaten 45-run stand for the seventh wicket.
"I was pretty motivated, it hasn't been a great season for us," Green told AAP.
"It was just really important to finish on a high, we both spoke about making sure we hit the middle of the bat and aiming at the sight screen.
"The rain made the ball skid on, so you find the middle of the bat and it just flies."
Maddinson, who spent the off-season battling testicular cancer which spread to other parts of his body, hit the winning run to backward square leg off Hassan Khan.
The Thunder (6-140) reached their DLS-adjusted target with four balls remaining.
The Renegades had finished their 20 overs at 8-170, left to rue a collapse of 3-7 that had restricted them either side of the drinks break.
Chasing a fast finish, the Renegades' call to tactically retire Mohammad Rizwan (26 off 23 balls) had also backfired as replacement Will Sutherland was run out at the non-strikers end.
Khan (46) played back to bowler Daniel Sams, who got a finger onto the ball before it slammed into the stumps with Sutherland (1) out of his crease.
To play finals from here, the seventh-placed Renegades must win their final two games and hope a slew of other results fall their way.
The Renegades' clearest path to the finals involves the Brisbane Heat losing one of their last two games and the Sydney Sixers falling in both of theirs.
Even if those results transpire, the Renegades will need to beat the second-placed Perth Scorchers and Adelaide Strikers and hope they can leapfrog the Heat on net run-rate.
The Thunder play the Sydney Sixers this Friday for their last game of the season and must win that match to have any hope of avoiding a sixth wooden spoon in 15 BBL seasons.
