The Strikers showed great sportsmanship, making the extraordinary move to withdraw their appeal and allow James Pattinson to bat on after confusion reigned over third umpire Greg Davidson's run out call.
In the end, the drama had little impact on the result as Alex Carey's 70 off 46 balls helped Adelaide reel in the victory target of 147 with five balls to spare.
Strikers' Jon Wells (24 not out) steered the visitors to 5-147 in front of 26,932 Gabba fans.
Earlier, Brisbane's James Peirson (24 not out) and rookie spinner Mujeeb Ur Rahman (27) saved Heat blushes with a 45-run last wicket stand after the hosts lost 7-23.
A Cricket Australia spokesperson said the long delay to clarify the call was caused by a "communication issue" between the third umpire and on-field officials.
"We experienced some communication issues between the third and field umpires who thought it was a mistake," the spokesperson said.
Earlier, Max Bryant showed glimpses of what he can bring to the table this season with22 from 20 deliveries.
Lynn top scored for the Heat with 33 off 20 balls while Strikers spinner Rashid Khan took 3-19.
Adelaide won the tournament's first "bat flip", a new innovation replacing the traditional pre-game coin toss, with Ingram correctly calling "roofs" and opting to field.
The Heat now shift their focus to the Hurricanes when they clash on the Gold Coast this Saturday night. Tickets are available through ticketek.