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Nweke snatched a long lob from player of the match Peta Toeava between the arms of the two Tactix defenders, and slotted the ball in just before the clock ran out.
The Mystics had the measure of the Tactix in the first quarter, led by captain Sulu Fitzpatrick from the back, putting pressure on shooters Ellie Bird and Jess Prosser.
At the other end, Nweke held her ground up against two of the world's best defenders, Jane Watson and Karin Burger, and the home side had a 5-1 advantage which quickly grew out to a six-goal difference.
Toeava was in everything on attack and defence, and the Mystics had a handsome 16-9 difference at quarter time.
The return of Tactix goal attack Te Paea Selby-Rickit from a pre-season ankle injury, entering the game in the second quarter, helped the Tactix attack.
Although she was only expected to play 30 minutes, she lasted 45 and ensured the Tactix won their first quarter of the season, and notched up their first point.
A full-court effort from the Tactix pushed Mystics midcourt into multiple mistakes, and the visitors capitalised; the defence of midcourters Kimiora Poi and Charlotte Elley standing out.
Selby-Rickit's presence opened up the Tactix shooting circle and they managed to draw even, but couldn't pull in front, down 27-25 at halftime.
But it was the first time the Tactix won a quarter in this year's league, and did so convincingly 14-9.
The Tactix continued the momentum after the break, and still forcing mistakes in the Mystics midcourt, they were able to draw level again.
The contesting for the ball from both sides was fierce, and with the Mystics up by three, the umpires stopped the game and called both captains in to warn them of borderline intentional infringing.
Fitzpatrick and Kate Burley took back control of the defensive circle and suddenly the Mystics' lead was back out to five. Then Watson and Burger responded at the other end, and the gap reduced to two again, 39-37, going into the final spell.
The Mystics made a big change – replacing Burley with Ama Agbeze at goal keep. They pulled away to five with 10 minutes left in the match.
When Erikana Pedersen left the court with an injury, and Samon Nathan replaced her at wing attack, the Tactix didn't miss a beat, again closing to two.
But Agbeze went hunting, pulling in a crucial intercept, which saw the Mystics take the upper hand again, but it was short-lived.
With one and a half minutes left on the clock, a wayward pass by Agbeze allowed the Tactix back in and they drew level 52-52 with 16 seconds to play. One more centre pass to the Mystics, and Toeava's practiced bomb into Nweke paid off.