Chasing 155 for victory on Friday night, the Sixers looked set to get the job done comfortably needing just five runs off the final Lucy Hamilton over.
That equation became a more shaky three needed off two balls following some beautiful death bowling from Hamilton.
And when Erin Burns was run out on the penultimate delivery attempting to come back for a second, it meant two runs were needed off the final ball for victory, or one run to send it to a Super Over.
Coyte strode to the crease with all the pressure on her, and she embraced the task at hand, squeezing a fuller Hamilton delivery just wide of the backward point fielder for a match-winning boundary.
The successful run chase was set up by opener Ellyse Perry, who struck 58 off 38 balls to help lift the Sixers to 1-103.
The loss of 4-27 put the pressure back on the Sixers, but a vital 21 not out off 14 balls from Alice Capsey got the required run rate back down to a manageable level.
And although Capsey was left stranded at the wrong end for the final delivery, Coyte showed nerves of steel to get the Sixers over the line.Â
Earlier, Georgia Redmayne scored 58 off 44 balls and Charli Knott (57 off 47) also produced a half-century as the Heat made 5-154.
Knott cracked five fours and three sixes while Redmayne registered eight boundaries as the Heat moved to 1-117 in the 15th over.
Ashleigh Gardner's dismissal of Knott, followed by Redmayne's departure a short time later didn't hurt too much, with Annie O'Neil (18 off 12) able to add some handy late runs.
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