Sydney Sixers 164 for 5 (Burns 51*, Ecclestone 47*, Bates 41) beat Brisbane Heat 163 for 5 (Jonassen 38*, Petersen 4-17) by five wickets
In reply to Heat's 163 for 5 in Wednesday night's top-of-the-table clash at North Sydney Oval, Sixers were in all sorts of trouble at 72 for 5 after 12 overs.
With them needing 92 off 48 balls, Burns (51 not out off 32 balls) and Ecclestone (47 not out off 25 balls) whacked the Heat attack to all areas of the park to seal a famous victory with three balls to spare.
The result extended Sixers' lead at the top of the table to three points over the second-placed Heat, who have only one match remaining. It means only the third-placed Hobart Hurricanes can still catch Sixers.
Hurricanes must win their remaining two games and hope the Sixers lose both of theirs in order to snatch the top spot. Whoever finishes on top secures a direct berth in the final.
It marks a remarkable turnaround for the Sixers, who collected the wooden spoon last season despite boasting a star-studded squad. Wednesday's result proved the fighting spirit within the side.
Sixers needed 12 runs off the final over and Ecclestone did the job by smacking Nicola Hancock for a six, a four and a two.
"I'm absolutely buzzing," Burns, who played a crucial role in getting the team over the line in her 100th WBBL match to continue an outstanding season in the middle order, said. "I'm just so stoked we got over the line as a team. It's always been a battle against Heat.
"You kind of dream of these moments to be able to get your team home. I'm not necessarily the one that got us home - Eccy [Ecclestone] bombing sixes and fours towards the back-end was beautiful to watch."