Thomas Rosicky put the Gunners ahead in the first half before doubling his personal tally just after the break to make it 2-0.
Arsenal held out, however, to claim the vital three points as they look to qualify for the Champions League next season.
Here, Sports Mole takes an in-depth look at an action-packed 90 minutes at The Hawthorns.
On target 5
On target 6
Was the result fair?
A draw would have been the fairest result in this match as, for large spells, it was a very even game. Neither side dominated and, although Arsenal enjoyed more possession than the Baggies for much of the match, both sides looked very capable of scoring throughout. Up until the 70th minute the Gunners may have just edged it but after Mertesacker's red card, it was one-way traffic and West Brom were unfortunate to come away with nothing.
West Brom's performance
The Baggies played well throughout, matching Arsenal for much of the game until Mertsacker's red card. They were a bit unlucky to go into the break 1-0 down and 2-0 was certainly a harsh scoreline. They had chances to score before the penalty, but they only have themselves to blame for not taking any of the chances they created in the final 20 minutes. They were rampant during that time, but the likes of Lukaku and Long both missed very good chances to find the equaliser.
The Gunners put in a very good away performance considering how hard it is to play at The Hawthorns. They looked to be fairly comfortable at 2-0 having taken most of their chances when they arose despite the Baggies putting up a spirited fight. The Mertesacker red card changed everything for the Gunners and suddenly they had to park the bus, but they showed that they can do this by holding out for all three points. That was partly down to poor finishing from West Brom, but the Arsenal defence also deserves some credit.
Sports Mole's man of the match
Thomas Rosicky: There were a few candidates for this award, but Rosicky's two goals edge him ahead of the rest. The Czech midfielder is starting to find form for the Gunners and he has developed a very slick partnership with Santi Cazorla. His first goal showed quick thinking to divert Gervinho's shot in, while his second showcased his fine first touch and subsequent shot, although it took two efforts to beat the goalkeeper.
This one has to go to Aaron Ramsey's miss in the first half. A two-goal deficit at the break would have been harsh on the Baggies, but Ramsey really should have provided it. Somehow it is even worse that it came at the end of a fantastic Arsenal move, which resulted in Giroud backheeling the ball to Ramsey in the box, but the Welsh midfielder missed the target from six yards out. A real sitter.
Howard Webb had a typically strong game. The big decision was the penalty and resulting red card for Mertesacker, but he really had no choice. It was a clear foul in the box that denied Long a goalscoring opportunity and Webb did exactly the right thing. He did miss a potential penalty for a foul on Yacob in the first half, but it wasn't exactly clear what had happened at first so perhaps he deserves the benefit of the doubt on that occasion.
West Brom: The Baggies are not scheduled to be in action again for two weeks when they will face Newcastle United at home.
Arsenal: The Gunners, meanwhile, will host Norwich City at the Emirates Stadium next Saturday.