Sam Allardyce's men could have extended the scoreline to reflect their dominance on the pitch but nevertheless had no trouble seeing off their non-league opponents
It did not take long for the Premier League side to assert their superiority over their Conference South opponents, as Ravel Morrison broke the deadlock in the 20th minute.
The former Manchester United midfielder coolly converted following James Russell's fine reaction save after Boreham Wood defender Ben Nunn had inadvertently deflected new signing Razvan Rat's cross goalwards.
|9/1||West Ham are 9/1 with Coral to be relegated from the Premier League
West Ham continued to dominate proceedings, with Rat and Paul McCallum - who scored in his side's 6-2 win over Cork City last Sunday - going close, but they went in at the break just two goals to the good.
Allardyce changed his entire team at half-time, with captain Kevin Nolan, Joe Cole and Matt Jarvis among those entering the fray.
Unsurprisingly, the addition of more first-team regulars to the away side's line-up only served to increase their stranglehold on the match.
Jarvis wreaked havoc down the West Ham left throughout the second period and he had a chance to increase West Ham's lead on the hour mark but could only fire over the bar after collecting a cleared Cole corner on the edge of the area.
Ex-Liverpool man Cole himself then went close with 10 minutes remaining, before skipper Nolan sealed the victory with a clever volleyed finish after 83 minutes.