Led by a tireless performance by captain Temepara George and the gun shooting of Samoan international Cathrine Latu, the Mystics sniffed an upset at Olympic Park before the hosts drew away in the final two minutes.
The Mystics trailed 54-55 with 2min 57sec left but made some crucial turnovers as the Swifts -- boasting four internationals -- got home thanks to the cool heads of shooting pair Catherine Cox and Susan Pratley.
"We had it (a win), but it was really good to see our fightback," George told NZPA.
"We had different combinations come on, we swapped some positions and it was about time we showed some fight right to the end. Just a couple of passes was all it took, and against a well-drilled Swifts team you can't afford that. "
Cox defied an ankle injury to shoot 29 of 33 and Pratley hit 30 from 34, while Latu was the most accurate on the night with an excellent 38 from 40 in a tense duel with goal keep Rebecca Bulley.
It was the fifth consecutive loss for a New Zealand side in Australia this year after none was successful in 2008.
It left the Mystics, who trailed 27-33 at halftime, in the lower reaches of the points table with just one win from four.
Competition favourites the Melbourne Vixens were the only unbeaten side after four rounds, with the Magic and Adelaide Thunderbirds rounding out the top-three and New Zealand sides the Mystics, Canterbury Tactix and Central Pulse filling the bottom three spots.
Mystics coach Te Aroha Keenan opted to rest her English international shooter Pamela Cookey in the first half, with Latu and 21-year-old Grace Rasmussen combining at the attacking end.
With George and wing attack Keshia Grant providing good service via the aerial route to the 1.89m Latu, the Mystics kept pace for much of the first quarter.
But the Swifts' international shooting pair Cox and Pratley were difficult to contain and only missed a solitary shot between them in the first quarter as the hosts claimed a 16-13 lead.
Keenan benched Grant after one quarter, shifted George to wing attack and handed Rawinia Everitt the centre bib but the Mystics were picked up for several infringements on attack and lost momentum.
The Swifts shot out to a 31-22 lead, with Pratley hitting her first 13 attempts in succession, before a late Mystics rally narrowed the halftime deficit to six goals.
Former Silver Ferns defender Vilimaina Davu was given a third quarter rest after a torrid first half battle with Cox, with Rachel Rasmussen adding more speed in defence, while Cookey was given her chance in the circle.
Rasmussen made an impact, and with Stephanie Bond disrupted the Swifts' shooters as the Mystics kept fighting to enter the final quarter trailing 41-46.
Swifts 59 (Catherine Cox 29/33, Susan Pratley 30/34) Mystics 55 (Cathrine Latu 38/40, Grace Rasmussen 7/8, Pamela Cookey 10/10). Halftime: 33-27.
