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.
Sam Allardyce's side had to see out eight minutes of stoppage time, following a nasty injury to Brighton's Gary Dicker.