The first-half goal saw Arsene Wenger's side prevent the Baggies from distancing themselves from the bottom three in a game where the hosts were rarely threatened
The Frenchman met Santi Cazorla's left-wing corner with a powerful downward header in the 14th minute, ensuring Arsene Wenger's men picked up their fourth league win in a row.
|VIEW FROM THE EMIRATES STADIUM
|By George Ankers
Arsenal could have applied much more of a killer edge to this match but, in what was essentially a dead rubber, they did what they had to and no more. Olivier Giroud got the goal by taking advantage of weak marking at a first-half corner - though a late confrontation with Graham Dorrans might see him under a little scrutiny after the game.
Mesut Ozil was the brightest spark, the man who least faded after the break, and Abou Diaby returned to the bench if not the pitch; the two biggest pluses for Arsene Wenger. The fans, meanwhile, were most concerned with loudly trying to convince Bacary Sagna to extend his contract.
West Brom looked more or less happy to take the nil as they were unable to make any kind of dent in the hosts' domination of possession but Pepe Mel's men had little about which to worry themselves.
West Brom, meanwhile, went into the game knowing they had likely done enough to secure safety, with 18th-placed Norwich City facing two difficult fixtures, and there was little intensity on show in a low-key affair.
Lukas Podolski did strike the post for Arsenal in the second half, but one goal proved enough as West Brom struggled to carve out opportunities.
Arsenal went in front just before the quarter-hour mark thanks to Giroud's firm header.
After Cazorla had seen his shot deflected over the bar by Youssouf Mulumbu, the Spaniard curled the resulting corner in from the left and Giroud got the better of Craig Dawson to plant a well-directed header into the net from six yards.
Graham Dorrans stung the palms of Wojciech Szczesny with a rasping drive in the 32nd minute, while Saido Berahino blasted a shot narrowly over a minute later.
The hosts' response was immediate, Cazorla bringing a smart save out of Ben Foster after running onto Podolski's cut-back.
Mathieu Flamini, back in the side in place of the rested Aaron Ramsey, hit a tame effort straight at Foster from the edge of the box as Arsenal ended the first period in the ascendancy.
In a quiet second half, Dawson headed over the bar from a corner in the 72nd minute before dragging a speculative effort well wide of goal from 30 yards shortly afterwards.
Mesut Ozil, quiet for much of the match, stabbed narrowly wide of goal after getting on the end of Giroud's flick as Arsenal looked to put the game to bed.
Podolski's mis-hit shot then rebounded back off the post and into the arms of a grateful Foster, but it mattered little.
While Arsenal's title hopes faded some time ago, the club can at least take some consolation from reaching their highest Premier League points tally since the 2007-08 season.