The Gunners were in control for most of the match, passing and running with the incisiveness that eluded them against Swansea last weekend. Yet both of their goals came from Mikel Arteta penalty kicks, and both were controversial.
Hardly anyone disagrees that the first should never have been scored. Santi Cazorla shamefully crumpled to the ground when Steven Reid whiffed with a lazy challenge, but referee Mike Jones did not hesitate to point to the spot.
Thereafter, it was Arsenal's game to lose, and they duly took care of business. When Alex Oxlade-Chamberlain went down in the 64th minute, Arteta sealed the game for a Gunners side that was remarkably composed and assured.
Here are six things we learned from their crucial bounce-back win.
It's usually difficult not to like Santi Cazorla when he plays. The little Spaniard plays with a determination and eye for the spectacular that can turn any boring game into a spectacle.
But his blatant dive to win Arsenal's first penalty was absolutely disgraceful. Arsene Wenger said after the match that he would look at the incident and consider having a word with Cazorla.
If Wenger is serious about disciplining his players, he will. Football doesn't need those kinds of disgraceful flops, and after an incident like this, there is a danger that Cazorla's reputation could precede him in the future.
Don't be surprised if the FA takes disciplinary action, and don't be surprised if Arsenal accept it without protest.
Arsenal have the third-best defense in the Premier League, but you wouldn't know it by watching their last few games.
Thomas Vermaelen and Co. have conceded far too many goals this season by committing unforced errors, but there were none to be seen against West Brom.
During the few occasions when the Baggies ventured forward, Arsenal kept a solid shape and rarely made the elementary mistakes that plagued them against Swansea and Everton.
Per Mertesacker's reading of the game was outstanding, both full-backs contributed at both ends of the pitch and, most importantly, Thomas Vermaelen looks like he's finally finding some good form. All that makes Arsenal's problems going forward easier to bear.
Perhaps it was because they simply had more time on the ball, but the Gunners were far more positive and pugnacious than in their last couple matches.
However, much of that is due to the extra rest that Arsenal got since their humiliation at the hands of Swansea last weekend.
Arsene Wenger left Jack Wilshere, Mikel Arteta, Santi Cazorla, Olivier Giroud and Per Mertesacker home for the match against Olympiacos in midweek, giving each time to recuperate in the middle of a hellish schedule.
The result was a more polished, complete effort at both ends of the pitch which had the continuous excitement that recent games have not. With the calendar set to be more kind before the new year, Arsenal could be well-positioned to put together a good run of results.
If Lukas Podolski had been fit enough to start, Gervinho would presumably have been played on the right wing and Alex Oxlade-Chamberlain would have had a great view of the action from the bench.
One would think that the German will be fully recovered by next week's match against Reading, and while he deserves to keep his place, Gervinho does not.
Oxlade-Chamberlain played superbly against West Brom, constantly racing down the right flank to whip in a cross or twist and turn past Goran Popov, whom he ran ragged all day.
That dynamism resulted in Arsenal's second penalty, which was conceded when Chris Brunt realized that he could not keep up with him in the box. There were other moments when Oxlade-Chamberlain was almost found by a through-ball, never allowing the Baggies a moment's rest.
Though he has been somewhat underwhelming in recent games, a performance like this deserves an encore.
By far, the biggest star of all against West Brom was Jack Wilshere, whose man-of-the-match display was his best since returning from injury.
He was the dynamic, tireless, box-to-box presence that Arsenal have sorely lacked recently. Rest helped him the most, as the determination of his lung-busting runs was matched only by the guile and intelligence of his passes.
A common sight was Wilshere bombing out of Arsenal's half and, when pressure came, finding the perfect little pass to keep play moving or spread the ball wide.
His instincts around the box kept several attacks alive, and he almost scored in the 90th minute with a shot that was blocked by Goran Popov.
Arsene Wenger said after the game that Wilshere took "a big step" toward getting back to the player he was before injury. Once he does, Arsenal will have one of the most valuable players in the Premier League.
Arsenal really should have won this game by a larger margin than they did. Numerous golden chances went to waste in the first half, and there were several served up on platters in the final 15 minutes (Lukas Podolski's miss of the season from six yards out comes to mind).
But often, what jump-starts a team out of a barren run is pure luck. It tends to desert teams that are going through hellish stretches and comes in buckets for those on the rise.
Finally, Arsenal got that luck against West Brom. They had numerous chances to win the game from open play, but, in the end, a massive mistake by the referee put them in the driver's seat. This time, the Gunners never took their foot off the gas pedal.
Arsenal can certainly be criticized for various flaws in their performance. Luck will not carry this team, which is just beginning its comeback, to the Champions League next season. But they now have a foundation on which to build their renewed top-four challenge.