With just five minutes played, a quick transition allowed Neeskens Kebano (30) to slip in Andreas Pereira (26), who smashed in his first Fulham goal from a tight angle above the helpless Łukasz Fabiański (37).
The visitors remained on top early on, and almost doubled their lead when Dan James (24) cut inside and struck the crossbar from range.
Gianluca Scamacca (23) linked up well with Lucas Paquetá (25), seeing his header saved by Fabiański and dragging an effort wide minutes later in what was turning out to be an action-packed first half.
The Hammers came even closer to an equaliser when Aaron Cresswell’s (32) lung-busting run ended with Scamacca heading towards Fabiański, before Jarrod Bowen’s (25) follow-up was turned behind.
The ensuing corner proved pivotal, as Pereira brought down Craig Dawson (32), having twice been warned by Chris Kavanagh, leaving Bowen to send Bernd Leno (30) the wrong way from the spot.
David Moyes claimed his side were “building momentum” ahead of kick-off, but it was Fulham in the driving seat, despite the level scoreline.
However, having failed to take his earlier chances, Scamacca made the most of Paquetá’s pick-out, delicately lobbing Leno inside the box.
The Italy international’s lack of celebration suggested possible wrongdoing, but following a lengthy VAR check, no offside or handball was evident.
In search of a way back into the contest, Tom Cairney (31) struck low from the edge of the box, but was denied by a well-timed Cresswell block.
Centre-back Shane Duffy (30) was desperately thrown on up front for the visitors, but the game was killed off after Tim Ream (35) and Leno got their lines crossed at the back, allowing substitute Michail Antonio (32) to pass into an empty net.
West Ham extend their unbeaten home streak to four in all competitions, while, despite suffering his second pair of back-to-back defeats since taking charge, Silva and his side remain 9th in the Premier League table.
Flashscore Man of the Match: Lucas Paquetá (West Ham United)
