Henriques' dismissal was part of a 4-12 collapse, after he had combined with a more circumspect Daniel Hughes for a 99-run third-wicket stand, before Steketee also had him caught in front of the wicket for 46 off 44.
The pressure began to show as Brad Haddin ran himself out for seven.
It left the Sixers needing 20 from the final two overs, and while Johan Botha (16) struck three boundaries from the penultimate over, the match took another turn when Sean Abbott was caught in the deep before Cutting's final-over heroics.
Earlier, Nathan Lyon was the Sixers' best with the ball, tearing through Brisbane's top order to claim 4-23 and leave the home side reeling in the middle overs.
McCullum (44) was the only man who looked comfortable but he faced just 10 balls in the first six overs as the Heat endured their slowest powerplay of the tournament at 2-40.
However a late flurry from allrounder Jack Wildermuth (29 from 16) took the Heat to 9-167, after he combined with Marnus Labuschagne (20) for a 26-ball 51-run seventh-wicket stand before Abbott (4-40) claimed them both in the final over to see the hosts finish 9-167.
"I think most teams would have lost that by five or six overs," McCullum said.
"But the belief in the group, we just kept fighting hard.
"In the end it's disappointing to run second but really proud of the boys for not just tonight but the entire campaign."
Meanwhile Henriques was disappointed his side had let the match slide to the super over. "We should have got home easier than we did," he said.
"It shouldn't have gone to a super over. The shot I played to get out - if I just did what I did in the super over the game would have been over a lot earlier."