Set 181 to win on Friday night at Marvel Stadium, the Renegades required 46 off the final four overs but held their nerve to book a first BBL final appearance.
Allrounder Dan Christian was the hero for the Renegades, blasting an unbeaten 31 off 14 balls after skipper Aaron Finch (44) set the foundations.
Christian survived a scare in the penultimate over when Jack Edwards spilled a tough chance at long on with the Renegades already six wickets down.
The Renegades had looked in deep trouble at 6-133 when Finch was clean-bowled while attempting to switch-hit Steve O'Keefe (2-22).
O'Keefe also dismissed Test opener Marcus Harris in the first over, while Sam Harper fell to Ben Dwarshuis after an aggressive 36 off 17 balls.
Cameron White, back in the XI after two games on the sidelines with a hamstring injury, joined skipper Aaron Finch at the crease and looked in good touch early.
But the veteran chopped onto his stumps off an Abbott delivery on 29, while Mackenzie Harvey and Tom Cooper soon followed.
Openers Josh Philippe (52 off 31 balls) and Daniel Hughes (52 off 32) earlier led the way as the Sixers posted 3-180 - the highest score at Marvel Stadium for the season.
The previous highest score at the Docklands ground was 150.
Teams had posted low scores on the ground's drop-in pitch all season but the Sixers wasted no time finding the boundary after being sent in to bat.
West Australian young gun Philippe proved the aggressor as Kane Richardson, the BBL's leading wicket-taker, went for 30 off his first two overs.
Hughes was gifted another life on 25 when Renegades wicketkeeper Harper fumbled a straightforward stumping opportunity with Hughes well out of his crease.
Both openers fell to legspinner Cameron Boyce (2-33) shortly after bringing up their half-centuries