Glenn Murray had given the Seagulls an early lead when he converted Anthony Knockaert's through-ball.
Chicharito equalised on the half-hour with a dribble inside the area and shot into the top corner.
Izquierdo restored Brighton's lead with a delightful curling shot from the edge of the area on 59 minutes and Gross made it 3-1 with a fierce strike.
The win takes the Seagulls 13th, level with the Hammers on 27 points.
Brighton: 10 Feb v Stoke (A)
West Ham: 10 Feb v Watford (H)