A Nedum Onuoha own goal opened the scoring inside the first five minutes, before Diafra Sakho netted in his fourth consecutive game to kill off the tie early in the second half.
Having also claimed victories off of Liverpool and Crystal Palace, the Hammers have set themselves up for a good run of form when the Premier League returns after the international break, and Stewart Downing - arguably West Ham’s best player this season - believes that a top 10 finish is well within their reach - if they become more consistent.
Speaking to the Evening Standard, Downing said: "If we consistently perform like we did against Liverpool and we did today, then we have a hell of a chance of being inside the top 10, if not further up.
"But we have to consistently do that. We let ourselves slip against Manchester United (last weekend's 2-1 defeat), but if we put a run together, we have got a good chance."
The Hammers have been missing a number of players in recent weeks, and their squad can only improve with the return of Kevin Nolan, Mark Noble and Cheikhou Kouyate in the middle of the park. With the fortnight break due to international action, the first-team squad could be back to full strength - with ties against Burnley and Manchester City awaiting at the end of this month.
Downing added: "The good thing is we have a good squad - we have injuries to come back. And I think this international break has probably come at a good time for us.”
Nolan is already on the return from injury, coming on for the final 15 minutes of action at Upton Park at Sunday, whilst Kouyate and Noble are yet to make the substitutes bench. English forward Andy Carroll is also out of action, having yet to have made an appearance this season, but the Hammers are still going strong. If they can return to full strength during the two-week break in Premier League action, there is no doubt that they can seriously challenge for a top 10 finish in the top flight this season.