The result left Arsenal fifth in the table on 54 points, behind Tottenham Hotspur – who play Aston Villa later – on goal difference but having now played the same number of games. Brighton moved up to 11th with 37 points.
"It has been a tough week, especially today because we wanted a reaction (to the defeat at Crystal Palace)," Arsenal manager Mikel Arteta told the press.
"It came in the second half, which is too late; we have to have the courage and personality to play much better and raise the level in the first half.
"We made it really difficult for ourselves. We were sloppy, we had no purpose to attack, we were really imprecise and didn't want to play forward."
Arteta rejigged the Arsenal starting line-up due to injuries and midfielder Granit Xhaka started at left-back, a decision that gave Arsenal no control in midfield and no cohesion in attack in the first half.
Brighton opened the scoring when a long ball found Mwepu on Xhaka's flank and with the Swiss international further upfield, Mwepu found space for a cutback to Leandro Trossard whose curling effort sailed past goalkeeper Aaron Ramsdale.
Arsenal thought they had grabbed an equaliser just before the break when Gabriel Martinelli headed home amid a crowd near the goal line, but it was chalked off after VAR spent four minutes looking at replays to rule the Brazilian offside.
A change in formation gave Arsenal hope in the second half but it was quickly snuffed out when Mwepu drilled a half-volley from the edge of the box into the back of the net.
Martin Odegaard halved the deficit in the 89th minute with a hopeful long-range shot that took a wicked deflection and looped over goalkeeper Robert Sanchez to give Arsenal a lifeline, but Brighton held on.
"I'm glad we won today, we needed the three points. Coming from six defeats is not easy," Mwepu said.
"We really believe in ourselves, we have the right mentality in the group and we showed what we could do today. The game plan was to win."