It was the fourth successive league game that Arsene Wenger's side have come from behind to win as Arsenal have made the most of a slump in form by bitter North London rivals to challenge their grip on third spot.
"Tottenham have got be watching over their shoulders now," man of the match Theo Walcott told Sky Sports.
"We are getting our jobs right, defensively we have been fantastic. We know we can always score goals... it's been an up-and-down season but it's the way you finish."
Visitors Newcastle went ahead in the 14th minute through Hatem Ben Arfa's low drive but their celebrations were extremely short-lived as Arsenal's man of the moment Robin van Persie struck to level the scores less than a minute later.
Arsenal were in danger of failing to turn their dominance into more goals before Vermaelen prodded home in the fifth minute of stoppage-time after Newcastle failed to clear.
Despite a series of misses by the likes of Gervinho, Van Persie and Tomas Rosicky, Wenger said he had never doubted that yet another comeback was on the cards.
"I said to my assistant [Pat Rice], one more attack and we will score," he said. "We caught them on a counter-attack on the final movement of the game. We got five minutes of extra-time and that allowed us to win the game."
The result left Arsenal in fourth with 52 points from 28 games, one behind arch-rivals Spurs whose stranglehold on third spot has loosened after three successive defeats. Newcastle stayed sixth on 44 points, five behind fifth-placed Chelsea.
Manchester United jumped above Manchester City at the top of the table after beating West Bromwich Albion 2-0 on Sunday as their title rivals lost 1-0 at Swansea City.
A few weeks ago Spurs had looked to have sewn up third spot and automatic Champions League qualification, leaving Arsenal and Chelsea battling it out for fourth spot, but a top-three finish for Wenger's side is now a distinct possibility.
Wenger's men were 12 points behind their North London rivals at the start of last month but thanks to the Van Persie goal machine and a resurgence in the form of Rosicky, who signed a contract extension earlier in the day, Arsenal are on song.
Much of Arsenal's threat against Newcastle came up the right wing where Bacary Sagna combined well with speedy Walcott, who peppered the area with tantalising crosses.
Despite the hosts' bright start it was Newcastle who made the breakthrough when Vermaelen gave away the ball and Demba Ba was able to set up Ben Arfa, who was given too much time to get the ball on to his preferred left foot.
Newcastle were given no time to savour the moment as almost immediately Walcott scampered down the right to cross for Van Persie who shrugged off his marker to crash in a low shot and notch his 33rd goal of the season in all competitions.
Arsenal continued to find a way past Newcastle but a combination of some good stops by goalkeeper Tim Krul and some fluffed shots kept the match balanced before a sizzling finale.
Alex Song found Walcott on the right and his cross was only semi-cleared to the on-rushing Vermaelen who netted from close range to snatch all three points from a disappointed Newcastle.
"It was a total commitment tonight to get something from a team that are really in form," Newcastle manager Alan Pardew said. "They pushed and they pushed and unfortunately we didn't have the legs left."
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