The Gunners required just six minutes to go ahead at the Emirates Stadium and their opener came courtesy of Alexis Sanchez, who turned away from Sandro before drilling a shot from 20 yards into the bottom corner.
Only a last-ditch block from a West Brom defender stopped Mesut Ozil from doubling the lead shortly afterwards but after a slow start, the Baggies almost found an equaliser when Gareth McAuley headed against the crossbar after meeting a James McClean corner.
The near miss sparked Arsenal back into life and seven minutes before the break, Sanchez netted his second when curling a free kick over the wall and into the bottom corner of Ben Foster's net.
Arsenal were quickly out of the traps after the restart but after a speculative effort from Olivier Giroud, they struggled to create openings and West Brom almost capitalised with a header from McClean which was saved by Petr Cech.
It took until midway through the second half for the home side to create anything else of note and again it came through Sanchez, who played in Ozil on the edge of the six-yard box but he was denied by the advancing Foster.
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That proved to be the last opportunity for the visitors and the Gunners dominated the closing stages with Joel Campbell shooting wide from 14 yards and Giroud being denied by the face of Foster.
They were forced to settle for just the two goals but the result could prove pivotal at the end of the season with the North London outfit now sitting four points clear of fifth-placed Manchester United, who had hoped that Arsenal would drop points in the race for a Champions League place.