Crofts scored his fifth goal of the season with a looping 72nd-minute header after Latics goalkeeper Lee Nicholls had made a terrific save from Jake Forster-Caskey's header.
Both sides were unbeaten in their last four Championship games and both were eyeing their third successive win and a step towards the play-off spots.
Wigan had the first sight of goal through Leon Barnett, who met Ben Watson's sixth-minute corner at the near post but drilled his shot well wide.
Moments later, Brighton stopper Tomasz Kuzsczak came to his side's aid twice, first parrying Chris McCann's header from Marc Albrighton's well-delivered cross and then collecting Emmerson Boyce's long-range effort.
The Seagulls nearly took the lead themselves when right-back Bruno Saltor volleyed at goal and Nicholls made a smart save on eight minutes to deny him.
Watson was then unlucky not to give the FA Cup holders an 11th-minute lead after completing a neat one-two with Marc-Antoine Fortune and blasting a shot just wide of goal.
On-loan Manchester United youngster Nick Powell was the next to test Kuzsczak, doing well to shake off his marker and fire a shot at goal, which the Polish stopper collected.
Saltor then received a needless 27th-minute yellow card for tugging Powell to the ground as Wigan looked to break forward.
Powell again nearly put Wigan ahead on 41 minutes, receiving Fortune's pass in the final third and drilling a long-range effort inches wide of Kuszczak's goal.
Just before half-time, Fortune went close after collecting a half-cleared cross on the left of the area, cutting inside and firing wide.
After the break, Oscar Garcia's men shot out of the traps, Ashley Barnes crossing from the left for an unmarked Forster-Caskey, who headed straight at Nicholls.
Callum McManaman burst into life for the Latics with a thundering long-range effort on 52 minutes that Kuszczak did well to save.
A lull developed with both sides putting on pressure in the final third but failing to create any clear-cut goalscoring opportunities and more fouls breaking up play.
That was until Wigan substitute Grant Holt shook off Gordon Greer to go one-on-one with Kuszczak but he put his effort off target with 19 minutes remaining.
Craig Conway nearly doubled Brighton's advantage after cutting inside and unleashing a stinging shot at Nicholls, who parried the effort wide.
Kuszczak came to Brighton's rescue on 90 minutes by parrying Holt's header from fellow substitute James McClean's cross just wide with a diving save, ensuring the Seagulls remain unbeaten on the road since September.