Evan Ferguson simply passed the ball past Bernd Leno to give Albion a half-time lead.
Pascal Gross strode through the middle to supply Ferguson with the ball.
Albion have dominated the midfield with Mahmoud Dahoud, Pascal Gross and Carlos Baleba looking like an excellent new formation.
Fulham’s best chance came when Willian flicked a ball for Bobby Decovdover-Reid who fired tamely over.
Igor Julio and the fit-again Adam Lallana have looked assured for the Seagulls.