The Irons' skipper crashed in his fourth goal of the season to lift his side to within three points of leaders Southampton.
Brighton's early-season pace-setters have, by contrast, tumbled down the table after their winless run was extended to seven games.
The Seagulls could count themselves unfortunate, though, having created a host of chances to cancel out Nolan's 17th-minute strike.
And they were architects of their own downfall after a bad mistake from Liam Bridcutt gifted West Ham what proved to be the winner.
Brighton manager Gus Poyet likes his team to play the ball out from the back, but not when they end up handing it on a plate to a player of Nolan's ability on the edge of the area.
Bridcutt's heavy touch allowed the midfielder to nick the ball off him, stride forward and lash his shot past his old Newcastle team-mate Steve Harper.
Veteran keeper Harper had only joined Brighton on loan a few hours earlier and obviously did not have time to get his bearings, standing far too close to his near post and offering Nolan the rest of the goal to aim at.
Yet in a game littered with errors on a slippery pitch, Brighton had already squandered a chance to go ahead when Winston Reid's slip allowed Craig Mackail-Smith a run at goal, but the Scotland striker's angled shot flew wide.
As the first half wore on Brighton grew in confidence, and West Ham were just about clinging on to their lead by the time the half-time whistle blew.
Ashley Barnes headed Matt Sparrow's cross wide, John Carew blocked a goalbound shot from Bridcutt and Craig Noone's drive hit the side-netting.
And in stoppage time West Ham's on-loan Arsenal keeper Manuel Almunia had to pull off a superb diving save to keep out Mackail-Smith's stinging volley.
After the interval Harper did well to deny Carew after a smart turn and shot, and substitute Freddie Sears fired wide.
At the other end Bridcutt's long-range effort did not trouble Almunia, although Mackail-Smith did when he slid into the Spaniard feet first trying to chase a long ball.
Almunia was able to continue and Sam Allardyce's side had to see out eight minutes of stoppage time, following a nasty injury to Brighton's Gary Dicker.
Allardyce's direct style of play may not have endeared him to some of the West Ham faithful, but a quick glance at the league table surely will.