Up by eight points heading into the final quarter, the Firebirds held onto their lead until the final shot of regulation time when Swifts goal shooter Sam Wallace-Joseph levelled the match at 62-all with just five seconds remaining.
In the extra 10 minutes, it was the visitors who proved too strong despite a flurry of Donnell Wallam Suncorp Super Shots as the Swifts secured a 77-73 win.
Wallam finished the game with an incredible 55 point haul including four two-pointers while Tippah Dwan recorded three Suncorp Super Shots in her 18-point haul as well as 14 goal assists.
Defensive duo Ruby Bakewell-Doran and Remi Kamo were also at their battling best against the Swifts' shooting trio of Wallace-Joseph, Sophie Fawns and English star Helen Housby in her 100th National League appearance.
In front of a raucous home crowd of 3724, the Firebirds began superbly with Macy Gardner holding her own in a physical midcourt battle as the Firebirds edged their way to a three-point advantage at the first turn.
That lead grew to five by halftime as the Firebirds repelled a Swifts' fightback before a sensational block by Kamo of a Fawns shot sparked a late flurry of goals to put the Firebirds in control.
The dangerous Housby began finding her range in the third quarter sinking three Suncorp Super Shots but the Firebirds were unperturbed with a Dwan two-pointer right on the siren ensuring the hosts were up by an impressive eight points in the final quarter.
With the Swifts turning the screw in the final term as they whittled down the Firebirds lead, Head Coach Bec Bulley thrust captain Kim Ravaillion into the fray.
The Firebirds had the ball in hand in the final minute with a one-point lead but couldn't keep possession as the Swifts pounced to send the game into extra time.
Wallam hit four Suncorp Super Shots from six attempts in the added period but the visitors hit a perfect 14 goals from 14 attempts in the bonus 10 minutes including another Housby two-pointer to secure the points.
The Firebirds now hit the road to face the Melbourne Vixens and West Coast Fever in back-to-back home games before returning home against the Mavericks on May 19.
Every Firebirds match is live and on demand on Kayo Sports and Foxtel.