Nichols' shot from distance flew past Mark Birighitti with only four minutes left to play, to give Wanderers a come-from-behind win.
It was rough on Birighitti, who had had a superb match to that point, but it was a thrilling denoument to a match which came to life in the final 20 minutes.
Envir Alovodic's opening goal, when he put away the rebound after Lee Ki Je's free kick hit the crossbar, shouldn't have counted.
Alivodic was offside when the free kick was struck, and the linesman initially appeared to agree, flagging as Alivodic celebrated. But after a chat with referee Stephen Lucas, the goal was awarded.
It was confusing, and Wanderers' equaliser had a hint of a "leveller" about it.
Substitute Brendon Santalab threw himself to the ground under little pressure from Milos Trifunovic, and Lucas pointed to the spot.
It was a shameful dive from the Wanderers attacker, but Andreu didn't mind. He tucked the penalty away to haul his side back into the game, before Nichols did the business.
The Jets had goalkeeper Birighitti to thank for being in the game at all.
Birighitti was superb in the first half for Newcastle and were it not for him, the Jets would have trooped back to the sheds with their tails between their legs.
A rasping volley from Nichols prompted Birighitti's first intervention, as he beat away the Wanderers midfielder's clean strike.
Scott Neville looked like he'd scored against his old club, but Birighitti made sure he didn't with another diving save.
Then, Nichols' cross looked certain to find Federico Piovaccari, but Birighitti came flying form his line to punch clear. For someone who lost teeth for the cause only three weeks ago, it was remarkable bravery.
With their keeper performing heroics, Newcastle finally came to the party as the half drew near to its conclusion.
Trifunovic, the hero of last week's comeback, headed over the bar, before a curling shot from his compatriot Alivodic went narrowly wide.
There was still time for more heroics from Birighitti, who made his best save in stoppage time, from Dario Vidosic.
The Wanderers No.10 should have scored, but instead Birighitti reacted quickly to make a save with his leg. On the counter, Trifunovic's shanked cross forced Andrew Redmayne to push the ball around the post, as the first half came to a helter-skelter finish.
Newcastle were cursing their luck early in the second period when Nigel Boogard nicked the ball in midfield, feeding David Carney.
The return pass from Carney found a Jets player in space, the only problem was it was Boogard, who blazed over the bar.
Wanderers' midfield looked as if they'd missed the start of the second half. Dimas, Andreu and Nichols couldn't get a foot on the ball as the Jets buzzed around with the intent missing from their first half display.
Carney sliced open the Wanderers defence again, but once again the wrong man was on the end of it. Ben Kantarovski, obviously on a high after scoring a rare goal last week, sliced horribly wide.
Trifunovic and Alivodic were both left high and dry in the middle, and they were furious about it.
Leonardo's jinking run saw Andreu scythe him down on the edge of the area. He had to before Leonardo went any further, but it came at the cost of a yellow card.
When Alivodic bundled home, it looked like the cost would be even greater, but Andreu and then Nichols had the last laugh.
Despite the late escape and a seemingly soft penalty that helped Wanderers draw level, coach Tony Popovic believed it was a well-deserved victory.
"I thought we controlled large parts of the game," Popovic said.
"It was a good game, it was a tough match, and that's what we expected.
"They are on nine points, full of confidence. It's not easy to come here, but we created some good opportunities first half, second half as well.
"Conceding that goal late on is always a test but the response was magnificent."
Popovic believed "the penalty was a penalty" but was confused about why the Jets goal was awarded.
Newcastle were left to rue missed chances, but Jets coach Scott Miller said his side got what they deserved.
"I think the intensity in and out of possession needs to be better, and we just need to be much better," Miller said.
"I just didn't think we were at the tempo we needed to be today, especially with the fans here to support the team."
Miller believed his side was gaining a free kick for simulation when the penalty was awarded, but said the decisions evened out over the game.
"As contentious as the penalty was, ours was contentious as well," he said.
"I've only seen that once and it looks like Enver's body is offside. They marry up."
Newcastle Jets 1 (Alivodic 73')
Western Sydney Wanderers 2 (Andreu PEN 80', Nichols 86')
Hunter Stadium, Newcastle
Referee: Stephen Lucas
Crowd: 14,886
Referee: Stephen Lucas
Crowd: 14,886
