The Scorchers had finished top of the group stage with the Sixers second, meaning they faced other in the Qualifer, with Perth comfortably winning that game to guarantee a home final.
“A great tournament, to win the first one to set up a home final was the best we played,” said Australia all-rounder Marsh.
“We’re really fortunate to have a group that have pretty much grown up together, we pride ourselves on our cohesion and we’ve won a lot of close games. It is an incredible franchise.”
Perth have now won six of the 15 editions of the BBL, claiming their first title in the 2013-14 season.
The Sixers are the second most successful BBL franchise, with three titles, and crushed defending champions Hobart Hurricanes in the Challenger to reach this final.
But losing the bat flip proved vital, with the pitch particularly tough to score on at the start, which was delayed by five minutes because of rain.
After Daniel Hughes fell for seven at the end of the second over, fellow opener Steve Smith tried to counter, but was dismissed for 24 off 13 balls when he was trapped lbw by Aaron Hardie.
Gloucestershire left-armer Payne, who was named player of the final, then ripped through the middle order, removing Josh Philippe, Lachlan Shaw and captain Moises Henriques to leave the Sixers 95-5 in the 15th over.
Australia fast bowler Jhye Richardson’s 3-32 and 2-29 from Mahli Beardman ensured there was no late onslaught, with Ben Dwarshuis run out attempting two off the final ball.
Marsh compiled 44 off 43 deliveries and Allen struck 36 off 22 to set the Scorchers on their way, with the four wickets they lost – Sean Abbott claiming 2-19 – proving mere consolation for the visitors.
With the run-rate not an issue, Australia wicketkeeper Inglis’ composed 29 not out off 26 led Perth to their target with 15 balls to spare.