Carey's elegant 101 from 62 balls underpinned the Strikers' 5/197 at Adelaide Oval on Thursday night.
In reply, Brisbane were all out for 115 in 17.3 overs.
The Heat suffered a horror top-order collapse of 4/6 in 13 balls - three of them falling to Adelaide quick Wes Agar. Agar finished with 4/27 to join Perth's Jhye Richardson as leading wicket-taker in the competition, with 21 victims each.
The Strikers also banked a bonus point as they climb from seventh spot to fourth with two games remaining before finals.
Carey struck the first ton of the tournament, reaching the milestone from just 60 balls featuring 10 fours and three sixes.
The left-hander is just the sixth batsman in BBL history to score two centuries, following Craig Simmons, Usman Khawaja, Luke Wright, D'Arcy Short and Aaron Finch.
"It was an important innings, we knew that tonight and the next two games are really important," Carey said.
"It's a really tight tournament so it's really pleasing to help the team get that victory that we were craving."
Carey was unfortunate not to carry his bat through Adelaide's innings - he was given out caught-behind from the second-last delivery when the ball struck his right forearm.
But the damage had been after featuring in brisk half-century partnerships with fellow opener Jake Weatherald (36 from 18 balls) and Phil Salt (26 from 17).
Brisbane's Test recall Marnus Labuschagne (2/20) was the only multiple wicket-taker - on consecutive deliveries across his two overs.
Labuschagne opened the batting in the Heat's run chase but quickly lost his partner Chris Lynn.
Lynn (17 from nine balls) cracked two fours and a six before being caught on the square-leg boundary from Agar's bowling. Labuschagne made 28 from 25 balls before being trapped lbw by Agar and two balls later the paceman dismissed Joe Denly (15 from 16).
Agar's double-strike left the Heat wobbling at 3/64 in the ninth over. And Brisbane's proverbial wheels came off completely two overs later when Adelaide's Peter Siddle (3/13) took wickets in consecutive balls.
Siddle dismissed Joe Burns (one from six balls) and Lewis Gregory (three from six) as Brisbane's chase ended in a crash.
The returning Michael Neser took an incredible one-handed catch to dismiss the final batsman Mitch Swepson as the Strikers claimed a convincing win.