The French striker showed coolness and class to slot in his ninth and most important goal of the season, give Albion their first league win of 2020 and cap a remarkable comeback.
Nicolas Pepe had fired the Gunners into a deserved lead with a superb curling shot with just over 20 minutes to go, but Lewis Dunk scrambled an equaliser over the line from close range to set up a barnstorming finish.
Maupay's winner was a sucker punch to the Gunners, who have now lost back-to-back games since the Premier League returned - results that surely make a late run to Champions League qualification very unlikely.
They may also have to navigate the rest of the season without goalkeeper Bernd Leno, who was stretchered off after landing awkwardly on his ankle in the first half following an aerial challenge with Maupay.
Maupay's role in the incident seemed to anger Leno's team-mates, some of whom became embroiled in a shoving match with the striker at full-time.
Leno joins defender Pablo Mari and midfielder Granit Xhaka on the sidelines, both of whom were injured in Wednesday's 3-0 loss at Manchester City.
There is no such negativity for Brighton, though. They appeared to come through the game largely unscathed and are now five points above the bottom three.
Brighton dig deep
Brighton were the first team to publicly voice opposition to games being played at neutral grounds as the debate raged last month about how the Premier League might conclude during the coronavirus pandemic.
With five of their remaining nine matches being at home, four of them against teams in the top half of the table (including Saturday's), the Seagulls need every advantage that playing on home turf brings.
But while the Amex was obviously lacking in fervent home support, this did not hamper Albion's appetite for the fight or ability to rouse themselves after a setback.
Pepe's opener was a hammer blow, especially coming at a time in the game when the league's three-month absence due to the coronavirus pandemic would have started to take its physical toll on the players.
But they dug deep and found parity through Dunk, who took advantage of some Arsenal hesitancy in their own box to poke the ball in after it had ricocheted his way.
Prior to that they had threatened rarely, with Aaron Mooy's low first-half drive their best effort.
They would have the final say, though, as Maupay gathered the ball from substitute Aaron Connelly before producing a deft, decisive finish. (BBC Football)