Rumors of a fan protest were well founded with many empty seats visible at The Emirates Stadium during an otherwise uneventful first hour which yielded few chances before Mesut Ozil curled in a 58th-minute opener.
Theo Walcott doubled the Gunners' advantage, finishing a slick passing move with a close-range finish 10 minutes later, before Olivier Giroud came off the bench and scored a sublime third to seal his side's second win in seven games.
"We come out of a difficult period and our confidence goes quickly and comes back slowly," Arsenal manager Arsene Wenger told the BBC.
"We are in the final sprint in the Premier League and consistency will be very important. We have a little handicap on the points front. We have fewer possibilities to drop points."
Arsenal have 54 points from 29 games -- four behind Manchester City, who have played a game more, in fourth.
West Ham, who suffered a fifth straight loss, are 15th with 33 from 31 and are just five points above third-bottom Swansea City, who they host on Saturday, and the drop zone.
The Hammers manager Slaven Bilic was given the support of the club's board this week after a poor run of form - which now stretches to five league defeats in a row -- that has dragged his side into the midst of the relegation battle.
"Of course we are (in a relegation battle). We don't have to hide it," the Croat told the BBC.
"It's not being negative, it's being realistic. I told the players to forget today -- we have big games ahead of us. It's a massive game against Swansea on Saturday. We are in a fight to keep our Premier League status. We have to start winning games.
"To get that confidence back is the key point. One win will change everything for us. Because three points at this stage of the season are massive," he added.
(Reporting by Tom Hayward; Editing by Ken Ferris)