© PA Photos
The hosts came close to taking the lead twice in the first 11 minutes. First, Gervinho flashed a volley across the face of goal after West Brom had failed to clear their lines, and then Santi Cazorla sent a 20-yard effort narrowly wide.
Chris Brunt provided the Baggies with their first real sight of goal, firing a low strike inches past the post.
The Gunners took the lead after 24 minutes when Cazorla went down in the box. Replays suggested that there was very little contact, but Mikel Arteta stepped up to make it 1-0 from the spot.
They should have doubled this lead seven minutes before the break after Gervinho found Jack Wilshere inside the box, but the England international put his shot wide from just six yards out.
© AP Photos
The hosts continued to push for a second after the restart, with Gervinho fluffing two attempts at goal in quick succession when he could have done better.
Arsenal were awarded another penalty just after the hour mark when Alex Oxlade-Chamberlain was brought down by Brunt. Arteta stepped up once again and sent it down the middle for a second time to double his side's lead.
The Spaniard almost claimed a hat-trick 10 minutes from time when he whipped in a free kick that flew just wide.
Romelo Lukaku could have got a goal back for the Baggies in the closing stages when he had a free header, but he could only nod wide from close range.
Lukas Podolski had a glorious chance to put the icing on Arsenal's cake late on having been found by Wilshere's cut-back, but he blazed his shot high over the bar.