In keeping their finals hopes alive, the sixth-placed Stars blasted past the Heat's modest 6-149 with 37 balls to spare on Sunday night.
The win moved them to within two points of the Adelaide Strikers (fourth) and Hobart Hurricanes (fifth).
Clarke (63) and Maxwell (37) crunched 104 for the first wicket before Marcus Stoinis (29no) and Hilton Cartwright (16no) went on a power-hitting spree at the finish to consign the embattled Heat to their fourth successive defeat.
Maxwell predominantly played second fiddle with the bat as Englishman Clarke dominated the powerplay and became the first player to notch five half-centuries this season.
They succumbed in quick succession as the Stars took an early power surge in a bid to improve their net run rate but Stoinis and Cartwright kept the Stars' foot on the Heat's throat.
The pair thumped five sixes between them from the combined 17 deliveries they faced.
Earlier, Maxwell snared 2-19 from four overs before taking a candidate for catch of the summer.
The Stars captain backpedalled from within the fielding circle, leapt high and snaffled Sam Heazlett's attempted shovel of Nathan Coulter-Nile with a magnificent left-handed catch at full extension.
After completing the catch, Maxwell put his hand over his mouth in disbelief.
Maxwell introduced himself into the attack after Brisbane bossed the powerplay and struck immediate gold, when Chris Lynn (28), in his 100th match, tried to take down the Stars skipper but only succeeded in miscuing a high catch to Coulter-Nile.
Import Ben Duckett (51) was watchful early before teeing off during the power surge after the Heat had stalled mid-innings.
Duckett was bowled by legspinner Adam Zampa (2-20) when he missed a reverse sweep as the Stars continued to go from strength to strength.
