French forward Maupay lifted the ball over substitute Gunners goalkeeper Emiliano Martinez five minutes into added time to earn a much-needed 2-1 win for relegation-threatened Albion.
Martinez was only on the field because first-choice keeper Leno was stretchered off in the first half with a serious-looking knee problem following a nudge from Maupay.
Maupay expressed remorse for the incident, although he was angered by the behaviour of unnamed members of the opposition. He had a long running feud with Matteo Guendouzi throughout the competitive contest and Guendouzi grabbed Maupay by the throat at the whistle.
"At half-time, I went to Arteta to apologise because I never meant to injure their keeper," Maupay said.
"I just jumped to get the ball maybe and I think he twisted his knee, I never meant to hurt him.
"I am really sorry. I apologise again and I wish him a speedy recovery."
Tempers ran high at full-time, with Arsenal midfielder Matteo Guendouzi appearing to put his hand on Maupay.
Maupay added: "Arsenal players need to learn humility, maybe sometimes.
"They have been talking a lot first half, second half when they were 1-0 up. They got what they deserved."
Albion's win completed a first league double over the Gunners to push them away from the bottom three and dent their opponents' pursuit of European qualification.
Maupay, who also claimed the winner at the Emirates Stadium in early December, struck after Seagulls captain Lewis Dunk scrambled home an equaliser to cancel out Nicolas Pepe's superb opener.
The importance of Maupay to this Albion side cannot be under-estimated. Brighton were chasing a number of targets to lead their line last summer but they opted for the Frenchman and paid Brentford an initial £16m to get their main.
Maupay has nine goals to his name so far and has made an encouraging start to his life in the top flight but remains determined to improve. Asked earlier this season if he was happy with his tally, "Not really, I always want more," said the Frenchman who has Argentinian descent on his mother's side.
At the age of 23, he and a number of talented youngsters at Albion - including Aaron Connolly, Leandro Trossard, Alexis Mac Allister and Steven Alzate - can improve even further. If Brighton can maintain their Premier League status this campaign, the future could be quite bright on the south coast
Potter admitted his side were perhaps fortunate to secure all three points but was delighted to end a run of nine league matches without success dating back to December 28.
"It feels amazing, a big three points for us," he said.
"Certainly coming from a goal down in the Premier League isn't easy to do without a crowd here to push us on. The boys found something in them, I am so proud of them, it's an incredible effort.
"We know where we are at, we know the margins are small in the Premier League and you have to turn them in your favour and that's what we have tried to do.
"Regardless of the table we have to keep fighting and that's what I think we saw today."
Arsenal boss Arteta agreed Maupay had not meant to hurt Leno.
"I believe that no player has the intention to hurt anybody and I believe in this case exactly the same. It was unfortunate," Arteta said at his post-match press conference.
"It's a knee injury - a hyperextension of the knee - and we have to assess the damage.
"He was in a lot of pain and he's still in a lot of pain but we'll have to wait until tomorrow at least to see how bad the damage is."
The Gunners had enjoyed the better of the play and squandered a number of opportunities, while Bukayo Saka struck the crossbar early on.
Arteta, whose side were beaten 3-0 at Manchester City in midweek, said he was unaware of the Guendouzi incident and felt his team could only blame themselves for another disappointing defeat.
"I haven't seen the reaction. (There were) a lot of players talking and getting together but I didn't know what happened," said the Spaniard.
"The frustration was that we have thrown the game away.
"We haven't competed like you have to compete in the Premier League. I think it was all our fault."
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