Glen McAuley, Curtis Jones, Tom Clayton and Liam Millar were also on the mark as Steven Gerrard's side made it two successive wins in Group D.
Reflecting on the win, Gerrard told Liverpoolfc.com: "We started pretty strongly and West Ham weren’t comfortable in possession and we pressed them really well.
"Glen [McAuley] got out first goal with a tap-in and the second was an individual effort from Rafa [Camacho] when he cut inside from the left and curled one into the roof of the net with his right foot. It was a great finish.
"Tom [Clayton] got out third goal when he connected with a ball played in across the face of goal.