The Gunners were 3-0 up inside the hour mark but a double from Anthony Vanden Borre gave the visitors hope before Aleksandar Mitrovic snatched a dramatic equaliser
A Mikel Arteta penalty and brilliant Alexis Sanchez volley put the Gunners firmly in command inside the first half-hour, and Alex Oxlade-Chamberlain looked to have sealed the points when he made it 3-0 on 58 minutes.
But Anderlecht were far from finished, and former Portsmouth star Anthony Vanden Borre struck twice - the second from the penalty spot - to give them hope before Aleksandar Mitrovic snatched a dramatic equaliser at the death.
The Belgians almost opened the scoring after eight minutes when Dennis Praet's effort deflected off Per Mertesacker and into the side-netting, but the hosts responded as the returning Aaron Ramsey - in for Mathieu Flamini – saw a strike blocked and Alexis struck a post before Chancel Mbemba clumsily brought down Welbeck having found himself the wrong side of the Arsenal man.
Skipper Arteta calmly lofted the ball past opposing captain Proto to give Arsene Wenger's side the lead and Alexis made it 2-0 with a fifth goal in his last three games soon after.
The former Barcelona man's long-range strike beat Proto at the near post to leave the visitors in real danger.
Arsenal's dream half ended with a scare as Ramsey sustained a knock to his lower back, but the Welshman emerged apparently unscathed after the interval.
Oxlade-Chamberlain made it three soon after with his first European goal of the season after some slack play from Sacha Kljestan in midfield.
The England international robbed the American and surged past Vanden Borre before slamming the ball beyond Proto, although the experienced full-back then did his best to sour things for Arsenal as he hit back within three minutes from close range.
Vanden Borre was on the end of Andy Kawaya's delivery to pull a goal back for the visitors before reducing the deficit to one from the spot following Nacho Monreal's foul on Mitrovic.
And Mitrovic proved to be Anderlecht's hero, capping a remarkable comeback by heading home Andy Najar's delivery to salvage the Belgians' second point of the group and gain some revenge for Arsenal's last-gasp 2-1 win in Brussels.