Tensions flared at the final whistle after Maupay, who was involved in an earlier incident with Arsenal goalkeeper Bernd Leno which saw the goalkeeper stretched off, celebrated with his Brighton teammates.
Pepe had opened the scoring with a stunning curling shot into the far top corner on 68 minutes. Moving in from the right, he launched the ball from his left foot around the defenders leaving Mat Ryan with little time to save it.
Brighton pulled one back just seven minutes later through Dunk. A short corner from Solly March saw the ball bounce around the box before Dunk got a foot to it and hammered it into the bottom corner.
Arsenal, who made five changes from the team that lost 3-0 to Manchester City on Wednesday, nearly opened the scoring after seven minutes when Bukayo Saka's right footed effort from just outside the box hit the bar.
Mikel Arteta was forced into a substitution just before half-time with coming on for Leno after a shove from Maupay saw the Germany international land heavily on his knee.
Speaking after the game, Maupay said he went to speak to Arteta at half-time to apologise for the challenge.
"Some of the Arsenal players need to learn a bit of humility," he added. "They were talking a lot in the first half, and in the second half they got what they deserved. Until the keeper gets to the ball, you never know what could happen, so I just went to get the ball. I think it was shoulder against shoulder - it's football, and there was contact. I never meant to hurt him and I'm really sorry he was injured."
Arsenal's top scorer Pierre-Emerick Aubameyang had a goal disallowed for offside after 53 minutes. The flag went up but Aubameyang continued on and put the ball in the net. Replays showed a tight VAR decision not to allow the goal.
The result sees Arsenal stay two point behind Tottenham while Brighton stay in 15th position, four points ahead of the relegation zone.