An inspired Nicklas Bendtner ended Arsenal's goal drought as bottom-of-the-table West Brom were swept aside.
The Dane's left-foot shot opened the scoring and gave the Gunners their first goal in five league games but Chris Brunt equalised with a free-kick.
Kolo Toure restored the visitors' lead, heading in Andrey Arshavin's free-kick.
Bendtner made it 3-1 with a crisp volley and he later hit the foot of the post as Arsenal dominated and boosted their Champions League hopes.
Arsenal's victory cuts their gap to fourth-placed Aston Villa, who occupy the last Champions League spot, to three points - although the Londoners have played a game more.
West Brom, meanwhile, are staring relegation in the face as their winless run is extended to six matches.
The Gunners started the match knowing that they could become the first club to record five successive goalless draws in the top flight.
With top-scorer Robin van Persie on the bench, Bendtner was charged with trying to end the Gunners' run without a goal.
And he did it almost immediately, when he cut inside from the right wing and curled a low, left-footed shot into the bottom corner to notch Arsenal's first league goal for 364 minutes.
But if the Gunners thought it was the first step to comfortably collecting three points, they were given a shock soon after.
West Brom hit back within two minutes after Luke Moore had been fouled by Johan Djourou and Brunt stepped up to drive the resultant free-kick through the Arsenal wall and beyond Manuel Almunia.
The equaliser served to lift the hosts' confidence but a spell of pressure brought no reward as Moore was denied by Almunia and, later, the striker headed over.
Bendtner had a chance to add to his tally but lashed wide after he had collected Emmanuel Eboue's scuffed shot.
West Brom's fans taunted him and his Arsenal team-mates by chanting "Champions League, you're having a laugh."
But it was Arsenal who were to laugh last as they took over the game almost completely from that point on.
After Eboue had smashed a shot off target and Arshavin had done similarly, it took a composed finish from Toure to restore Arsenal's lead as he headed in Arshavin's free-kick from the left.
The defender then turned provider, launching a long ball over the top for Bendtner to control with his knee and then crack a volley into the far corner.
But Arsenal's recent profligacy was in evidence after the break when they managed to miss a host of chances.
Russia international Arshavin should have opened his account but was twice denied by Scott Carson, after Bendtner had created the chances.
Substitute Abou Diaby was next to take aim, but his shot was deflected over and shortly after Eboue shot straight at Carson from 12 yards out.
In between those opportunities, Bendtner came within a whisker of completing his hat-trick when he drifted across the edge of the penalty box before striking a low shot that cannoned back off the post.
By that stage West Brom had long looked a beaten side but they might have given themselves hope late on had Marc-Antoine Fortune squared the ball to an unmarked Moore rather than fire harmlessly across goal.
Arsenal missed yet another chance for a fourth goal late on when Arshavin's shot from inside the area was well saved by Carson.
West Brom manager Tony Mowbray:
"We won't win matches if we defend like we did in the first half.
"The defending has got to improve. I take responsibility for the fact I bought all the players in, but the defenders are not stepping up.
"I am frustrated. We work on it - we don't just wash things away. I have changed the individuals, but the goals are still going in against us."
Arsenal manager Arsene Wenger:
"Bendtner is improving from month to month. He will be better every three, six months.
"He has shown tonight he has the talent to be an Arsenal player.
"That is the right way to mature. I liked his presence. I liked his determined attitude and the way he took people on. That shows he has improved."