The win had significant ramifications ahead of next week's finals, ending the Sixers' three-game winning streak and meaning Hobart will finish top of the ladder.
That means the Hurricanes will host the final on Saturday week. Adelaide will host Hobart tonight at Karen Rolton Oval, with the Strikers needing an upset win to stay in the top-four hunt.
By winning their last regular-season game the Renegades also improved to fourth, while the Sixers are third.
But the Renegades must sweat on other results to find out whether they play in the finals.
Chasing 131 for victory, Wareham (49 not out) and Webb (33no) took the Renegades to 4-134 from 16.2 overs on Friday in Melbourne.
The pair put on a whirlwind unbroken 85-run stand, rescuing the Renegades from a wobbly 4-49 in the 10th over.
Wareham, who earlier took three wickets, finished with a furious flourish, cracking five fours and two sixes from her 29 deliveries.
And Webb also found the boundary four times as the Renegades (five wins, five losses) climbed from sixth to fourth on the table.
The Sixers (five wins, three losses) remain third after failing to capitalise on an Ellyse Perry special with the bat.
Perry top-scored with 65 from 47 balls but the Sixers struggled to 9-130.
The allrounder dominated Sydney's innings, hitting nine fours and a six, despite frequently losing partners.
Only one other teammate - Ash Gardner (16) - reached double figures amid some excellent legspin bowling from Wareham (3-21 from four overs).
Alyssa Healy made a six-ball duck and the middle order failed to fire around Perry, who was dismissed in the 18th over when caught at long-on from the bowling of Alice Capsey (2-27).
The Renegades hit early trouble in their chase when Maitlan Brown snared two wickets in the second over.
Opener Davina Perrin (28 from 27 deliveries) and Capsey (10 from 15) briefly steadied before both fell in a three-over patch, leaving the Renegades in serious strife four down.
But Wareham and Webb launched a power-packed counter-punch with Brown (2-45) the only multiple wicket-taker for the Sixers.
All three games over the weekend will affect the top-four finishing order. The Melbourne Stars are second and on Saturday cannot afford a slip-up when they host the Sydney Thunder, who are out of finals contention.
The late Saturday game will feature fifth-placed Perth at home against bottom side Brisbane, while the Sixers host Adelaide on Sunday in a massive end to the regular season.
Only three points separates the Stars from the sixth-placed Strikers.
Tuesday's knockout final will feature the third-placed team at home against fourth.
The winner of that game travels to the second-placed team on Thursday for the challenger final and that will decide who faces the Hurricanes for the title.
