Trifunovic's goal ended a 566-minute drought, falling 41 minutes shy of the Knights' 607-minute record, set in the 2006. More importantly, the three points lift the Jets above the injury-ravaged Phoenix into seventh spot, just four points adrift of the top six.
Pained by a six-game goal drought, Miller's decision to change his formation to two strikers proved a masterstroke. Both Trifunovic and Carney got plenty of ball, and combined for a total seven shots between them.
Captain Nigel Boogard thought he was the one to open the scoring when his second effort was fumbled by Phoenix goalkeeper Glen Moss over the line.
But referee Jarred Gillett instead pointed to the spot after watching Trifunovic get pulled down as Carney's fifth minute free kick curled into the area.
The chances continued to come for the hosts in a free-flowing first half, and they almost extended their lead to three when right midfielder Enver Alivodic had his header cleared off the line by Andrew Durante.
The game changed when Kantarovski was shown his second yellow card for a dangerous challenge on Vince Lia in the the 58th minute, which followed a caution for his hack on Roly Bonevacia.
The Jets were forced to defend for most of the second half, but Carney stunned the Phoenix on the counter, showing a clean pair of heels to run onto an Alidovic's 66th-minute through ball.