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."
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.
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.
Knowing victory would put Arsenal within touching distance of Spurs having been 12 points behind them at the start of last month, Arsene Wenger's side made a lively start to the match.
Bacary Sagna combined well with speedy Walcott up the right to create much of the Arsenal threat and the Londoners could have been a goal up when the pair set up Van Persie who made a rare hash of getting to the cross.
Instead it was Newcastle who made the breakthrough when Arsenal defender Vermaelen gave away the ball and Cheick Tiote capitalised to send it through to Demba Ba who set up Ben Arfa wide on the right.
The Frenchman was given too much time to get the ball on to his preferred left foot and he unleashed a sweet shot into bottom corner at the near post.
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.
While Arsenal dominated proceedings with their patient build-up play that owed much to the distribution skills of Tomas Rosicky, who had signed a new deal earlier in the day, Newcastle looked dangerous on the break.
Walcott was again at the heart of things when Arsenal went close to doubling their lead early in the second half as his pinpoint cross from the right found Rosicky, whose header was tipped away by Krul.
Van Persie spurned a golden chance when his first-time shot from a Mikel Arteta cross went straight to Krul, while Rosicky fluffed a shot midway through the second half after being set up by Walcott.
Gervinho, Walcott and Vermaelen all went close in the dying minutes before the latter sprinted up the field to slam in the late winner.
Arsenal's recent form is in marked contrast to the start of the season when they took just four points out of a possible 15 to spark media talk of a crisis at the club, while it has coincided with a downturn in fortunes for Spurs.
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.
