The visitors had Adam Virgo sent off in the 48th minute but they produced dogged defending and had goalkeeper Michels Kuipers in outstanding form to repel everything Oldham could throw at him.
Kuipers made a serious of saves to thwart the home team's chances of moving up from fourth place in the League One table.
He helped struggling Brighton end a four-match losing run in league and cup as Oldham grew increasingly frustrated and also lost captain Sean Gregan with a nasty mouth injury near the end.
The game burst into life and controversy within the first eight minutes after Brighton defender Virgo was adjudged to have tripped Chris Taylor deep inside the box.
Referee David Foster awarded a penalty, but Virgo was convinced his opponent had dived and angrily shoved Taylor in the chest.
He escaped with a yellow card while Oldham's Lee Hughes was also booked for his part in the melee which followed.
Meanwhile, veteran winger Andy Liddell kept his head amid the drama and slotted the penalty into the bottom-right corner as Kuipers dived the wrong way.
Kuipers then saved a low shot from Hughes, but Brighton pulled level from their first attempt on goal as top-scorer Glenn Murray ran on to Steve Thomson's ball over the top and crashed in a superb drive from 14 yards.
Oldham went back on the attack, but Kuipers denied Mark Allott and made two stops from Taylor, the second a stunner as he reached up into the top corner.
Brighton missed a chance through Nicky Forster, only to lose Virgo just after half-time when he received his second booking for a needless foul on Chris O'Grady.
They still went close after 56 minutes as Andy Whing's header had to be cleared off the line, but Kuipers against came to the visitors' rescue when he parried O'Grady's 20-yard blast.
The Dutchman pulled off yet another fine save from Taylor before Oldham lost their attacking impetus.
Brighton could even have snatched it in the last ten minutes when substitute Stuart Fleetwood just failed to connect with Forster's low cross.