A second-half Andy Najar header (71) looked certain to hand the visitors an embarrassing defeat and give the well-organised Belgians victory and second place in Group D.
But Kieran Gibbs got forward from left-back to volley an equaliser (89) and substitute Lukas Podolski slammed in his first of the season (90) to get Arsenal out of jail on Arsene Wenger’s 65th birthday.
The result will scarcely paper over the cracks of an unconvincing performance, but Arsenal now have a five-point cushion on their nearest challengers for a knockout place, and group leaders Borussia Dortmund remain just three points clear.
Few in the travelling support could have foreseen such an ending on a night when – the energy of Alexis Sanchez aside – there was little to celebrate for 88 minutes.
Sanchez created an early, spurned chance for Santi Cazorla – about the only opportunity of note during a nondescript first half – and continued to provide his side’s spark during a second half which opened up as it wore on.
The Chilean deflected Cazorla’s free-kick too close to goalkeeper Sylvio Proto, whose one-handed stop from a Cazorla cross-shot moments later was all his own work.
Aaron Ramsey, otherwise quiet on his first start since last month’s north London derby, shot wide of the near post after more enterprise from Sanchez, but the half-chances represented rare moments of incision rather than a pattern of convincing Arsenal dominance.
Anderlecht’s confidence grew, and when Dennis Praet escaped the attentions of makeshift centre-half Nacho Monreal to dig out a cross, Calum Chambers was never close enough to prevent Najar heading down and beyond Emi Martinez: the ninth game in 10 Arsenal have conceded.
Their young keeper had been a spectator for the most part, but in a frantic finish he watched Anthony Vanden Borre miscue against the bar and benefited from Matias Suarez’s poor touch when the home sub was clean through.
Anderlecht paid a heavy price for that piece of miscontrol: Gibbs made a late appearance in the box to side-foot in Chambers’ cross before Podolski won it, smashing in from close range as a centre from Sanchez rebounded obligingly at his feet.