Arsenal have now mathematically qualified for next seasons Champions League.
This follows Chelseas 2-2 draw at Aston Villa on Saturday night.
Unai Emerys men, who are also looking to qualify for the Champions League, took the lead through Marc Cucurellas own goal.
Rogers doubled their lead before the break.
But Chelsea fought back through goals from Noni Madueke and Conor Gallagher.
The result leaves Villa on 67 points with three games left.
Arsenal, who are on 77 points, have four fixtures left and travel to Tottenham Hotspur on Sunday.
EPL: Chelseas 2-2 draw with Aston Villa sees Arsenal qualify for Champions League
