The Gunners looked to be in complete control of the contest as a penalty from Mikel Arteta and strikes from Alexis Sanchez and Alex Oxlade-Chamberlain put them 3-0 ahead before the hour mark.
But two goals in 10 minutes from Anthony Vanden Borre pulled the visitors back into the contest before substitute Aleksandar Mitrovic grabbed a dramatic equaliser in the 90th minute.
Arsene Wenger’s side are now five points behind group leaders Borussia Dortmund with just two games left to play.
The save looked as though it would prove pivotal as the Gunners soon started to assert their authority. After Alexis smacked the post from a tight angle, the hosts won a penalty midway through the half when Chancel Mbemba brought down Danny Welbeck in the box. Arteta made no mistake from the spot as he coolly placed his effort down the middle.
Minutes later it was 2-0 as Alexis netted Arsenal’s 500th goal at the Emirates. The Chilean won a free-kick on the edge of the box after a brilliant run and then continued his superb goalscoring form by lashing a volley into the bottom corner after his initial effort hit the wall.
Welbeck almost made it 3-0 before the break as he broke clear but a fine recovery tackle from Mbemba denied him just as he pulled the trigger.
Nevertheless, it didn’t take Arsenal long to add to their lead after half-time as Oxlade-Chamberlain curled a fine shot into the far corner shortly before the hour mark.
At that stage it didn’t look a question of whether the Gunners would win, but how many they would win by.
But Anderlecht had other ideas and they soon pulled a goal back when a ball across the six-yard box was tapped in by a wide open Vanden Borre, who was at least a yard offside.
The goal gave the visitors renewed hope and they were soon celebrating again as substitute Mitrovic was dragged down in the box by Nacho Monreal and Vanden Borre converted the penalty.
Welbeck and Alexis both went close for Arsenal before the goal but at 3-2 the momentum was firmly with the Belgians and they grabbed a dramatic equaliser in the final minute of normal time to snatch a point.
Andy Najar whipped in a fantastic ball from the right wing and Mitrovic beat his marker to head past Szczesny.
Arsenal could not rouse themselves in added time and the final whistle was greeted with boos around the Emirates as the realisation of another second-place finish set in.