Brown hit 53 from 38 balls to set the tone for the Heat before player-of-the-match Johnson took the best-ever figures in a BBL final with 4-26 to wipe out any hope the Sixers had of chasing down the target.
“I don’t think it’ll sink in for a while,” Johnson said.
“That’s something that you don’t go into games thinking about. You just want to hopefully contribute and hopefully win.”
After a slow start when he hit three runs from his first 10 deliveries, Brown exploded after the powerplay to bring up 50 in 32 balls.
The right-hander hit three sixes off Hayden Kerr, with two dispatched over long on and another over backward square.
His innings allowed Max Bryant (29 off 19) and Matt Renshaw (40 from 22) to finish strong.
Brown was eventually lbw on review when replays showed a Steve O’Keefe ball hit his pad before he cut it to point, making him the retiring spinner’s 99th and final BBL wicket.
The 30-year-old only debuted last season, but has now attracted offers from overseas clubs in the UAE and Bangladesh since hitting 12 sixes in his 140 against the Strikers on Monday.
The only rise more rapid than Brown’s is Johnson’s, who debuted in the BBL aged 27 last summer and has since played for Australia.
Wednesday night was a reminder of why.
The left-armer, who was named man of the match, broke the back of the Sixers early when he bowled Jack Edwards for 16 after the Sixers had taken 13 runs from the first five balls of the over.
He also bagged the key wicket of Josh Philippe for 22 when the right-hander was caught at mid wicket, before returning to remove Ben Dwarshuis and Hayden Kerr with his pace and bounce.
Johnson’s wickets stunted any hope the Sixers had of chasing down the target, with COVID-battling captain Moises Henriques the only batter to reach 25.
Mitchell Swepson (2-19) also sent down the best ball of the game, beating Jordan Silk with flight and turn to have him stumped for a fourth-ball duck.
The Heat’s win comes after they were beaten in the final over of last year’s final, while the Sixers remain stuck on three titles from seven appearances in deciders.
Sean Abbott held the hosts together with the ball with 4-32, but they were always facing an uphill battle chasing 167 on what has been a low-scoring ground this season.
“It’s a bit disappointing,” vice-captain Daniel Hughes said.
“We had a great year, so we can’t we can’t be too upset with how we played this year. We just didn’t get it right tonight.”