A week after scoring his first A-League goal, Wanderers striker Frederico Piovaccari added to his tally on nine minutes to put the home side in front.
That goal was cancelled out by the unlikliest of sources after Phoenix defender Manny Muscat scored just his fourth goal in 174 appearances to pull the New Zealand side level.
But they were denied a point in the 85th minute when Bridge smashed in the winner from close range to extend an impressive winning run for Western Sydney.
Coming off three straight victories and in front of 14,426 fans at Parramatta Stadium, the Wanderers made a bright start to the contest and had the Phoenix defence under pressure early on.
While it was the visitors who had the best chance inside the opening 10 minutes after a Michael McGlinchey free-kick struck the crossbar, Western Sydney broke the deadlock from the ensuing counter attack.
Mitch Nichols released Bridge, who was all alone inside Wellington's half. The forward sprinted into the area and squared the ball for Piovaccari, who tapped in from close range to score his first goal at home for the Wanderers.
The hosts continue to create openings and while Bridge had a shot saved by Glen Moss, a stunning Scott Jamieson strike was only ruled out by a foul in the buildup.
But against the run of play Phoenix hit back. Defender Muscat recevied the ball on the edge of the box and cut inside before unleashing an unstoppable low drive to make it 1-1.
The Wanderers had a good chance to go in front before the break when Dimas found Dario Vidosic inside the box from a free-kick on the edge of the area. Vidosic struck the ball first time, but Moss was equal to it.
Western Sydney were still the more dangerous side after the interval, yet it was Phoenix who came closest to scoring when the home side failed to clear a corner and substitute Alex Rufer hit the post with a well-struck volley.
Wanderers were still looking the most likely and they finally re-took the lead five minutes from time. A near-post flick-on from a corner was expertly taken down by Bridge, who beat his defender before slamming in the winner from close range for Western Sydney.
Western Sydney have won four straight A-League games for the first time in two seasons with coach Tony Popovic warning the influential Bridge is set to hit peak form.
"That's just his second start this year after a long (groin) injury in the pre-season," Popovic said of Bridge, who also scored in his first start last week against Melbourne City.
"We expect him to only get better."
"To win a really tough game - that wasn't easy out there. I don't think we were at our best but overall I think we deserved the win and it was good to get it late on."
Meanwhile Piovaccari was on the scoresheet again after scoring his first goal last week.
"It's because his fitness has improved, that's the big difference," Popovic said.
"Today you can see he's getting more powerful ... he was up against two very good defenders but he looked dangerous a lot more often."
While Wellington almost secured a point, there were moments when the Phoenix hung on by the skin of their teeth, no more so than when the Wanderers had four clear first-half chances inside five minutes.
"We weren't playing very good football," Wellington coach Ernie Merrick said.
"We normally control the midfield pretty well. I don't think we could hit a pass tonight. We had three strikers up front and we couldn't get Jeffrey (Sarpong) in the game."