Only the woodwork denied them a second killer goal before Arsenal, who apart from Alexis Sanchez had been insipid throughout, suddenly woke up to the fact that their Champions League campaign was coming off the rails.
In the 89th minute Calum Chambers launched a high cross from the right and left back Kieran Gibbs connected with a stunning left-foot volley without breaking stride.
That silenced the home crowd but a minute later their heads were in their hands as Sanchez wriggled through in the area and his cross fell to substitute Lukas Podolski who thrashed home the unlikeliest of winners.
It was rough luck on Anderlecht who suffered a sixth successive home defeat in the competition, while Arsenal, despite playing as poorly as they did in a 2-0 defeat at Borussia Dortmund in their opening match, gleefully took the points that kept them on course for the last 16.
Their manager Arsene Wenger could probably have found less stressful ways to celebrate his 65th birthday.
Defeat would have put Arsenal's slow-starting season under more scrutiny, as it was the Frenchman could afford a smile.
"In the second half we opened ourselves up and got caught," he told Sky Sports. "The crucial point was when it was 1-0 they couldn't take advantage of the chance to score the second and we kept going and managed to score two good goals.
"Anderlecht played well tonight and showed that this country produces top class players.
"It was vital for us because we are in a strong position to qualify now," added Wenger, whose side are second in Group D with six points, three behind Dortmund but five ahead of both Anderlecht and Galatasaray.
"If we win our home games we are through."
With Anderlecht at home next, Arsenal should qualify for the knockout rounds for the 12th consecutive season, but should they do that they will need to raise their game against the big guns.
NOISE LEVELS
Neither side managed a shot on target in a forgettable first half. Santi Cazorla fluffed Arsenal's best chance while Gunners keeper Emiliano Martinez, making his Champions League debut in the absence of suspended Wojciech Szczesny and injured David Ospina, had precious little work to do.
After the tepid first half fare the second period began in more promising fashion with Ibrahima Conte raising the noise levels with a shot deflected wide.
Arsenal responded minutes later when Sanchez found himself unmarked with his back to goal in the six-yard box but he failed to angle his header away from grateful keeper Silvio Proto.
It was the hosts who made the breakthrough though with 19 minutes remaining and it was goal of real quality.
Najar played the ball to Dennis Praet who twisted and turned Arsenal's lumbering defence before clipping the perfect cross to the far post where Najar dispatched a firm header past Martinez.
It almost got better for Anderlecht when Anthony Vanden Borre's miss-hit shot looped against the post with Arsenal's defence playing the role of statues.
Sanchez then rustled the side-netting with a free kick but Anderlecht looked the more likely to score as the crowd began chanting 'ole's' with every successful home pass.
It all went sour for Anderlecht though as first left back Gibbs produced his moment of quality and then, revived, the visitors sensed a smash and grab raid.
With the clock ticking to 90, Podolski, who had only been on the pitch for six minutes, stole the points.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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