It was just the result Arsenal wanted ahead of the most important European game in their history - the Champions League semi-final first leg against Villarreal on Wednesday.
They escaped without further injuries too. Broken nose victim Sol Campbell is their only definite non-starter, though teenage midfield general Cesc Fabregas is doubtful because of a foot injury.
But Arsenal remained in fifth place despite their victory, four points behind arch-rivals Tottenham, who visit Highbury next Saturday.
West Brom, by contrast, stay 19th, a point behind Birmingham and four behind Portsmouth. They have not won for nine matches.
Manager Bryan Robson had said that their season had "come down to five games". They have just four to save themselves now.
Certainly West Brom fought hard, and they were unlucky not to win a penalty after Pires had restored the Gunners' lead. But they lacked the quality to match an Arsenal side whose minds often seemed elsewhere.
The Gunners probed from the start. Abou Diaby broke into the box after five minutes, then surprisingly opted to pass rather than shoot and Albion scrambled the ball clear. Mathieu Flamini then shot straight at Tomasz Kuszczak, as did Alex Hleb, then Diaby.
Quashie gave Arsenal a fright with a tenth-minute shot that sent Jens Lehmann scrambling across goal. It was a rare moment of quality for the visitors.
Robin van Persie slipped as he ran onto Hleb's 23rd-minute pass, but Thierry Henry found Jose Antonio Reyes, whose shot was deflected wide by Neil Clement. Kuszczak then raced out to head clear as Henry threatened.
Robson came out of the dug-out to urge his centre-backs to concentrate. Clement responded with a tackle that forced Henry to fire wide after Gilberto's pass had played him through. Gilberto, stretching, then failed to connect with van Persie's cross.
Hleb made the breakthrough a minute before half-time. The Belarus midfielder took Reyes' pass, played a one-two with Henry and finished with a blast into the roof of the net.
The Gunners continued to press after the break. Curtis Davies made an important tackle to halt van Persie's run, then did the same to Henry. Kuszczak dropped a cross but Philippe Senderos could not take advantage.
Van Persie's shot on the turn was blocked by Quashie before Martin Albrechtsen rescued Albion after Henry had robbed Clement. It was the Frenchman's last action before he was rested with the Villarreal game in mind.
Kuszczak then rushed out of his area again to head clear from Henry's replacement Emmanuel Adebayor.
Van Persie fired against the wall and gained a corner but Gilberto, arriving late, headed the kick wide.
Arsenal then made a double 71st-minute substitution - bringing on Bergkamp and Pires for van Persie and Hleb. The move seemed to distract them and, seconds later, Quashie hit a low 20-yarder that skidded past Lehmann and into the net.
However, Albion were level for just four minutes. Adebayor found Pires, whose shot was parried by Kuszczak only for Bergkamp to turn the loose ball back for Pires to sweep into the net.
Albion had to pile forward. But when Davies fell under Emmanuel Eboue's challenge, referee Mike Dean waved away their penalty appeals.
It was a crucial decision, and Bergkamp took full advantage as time ebbed away. The Dutchman collected Eboue's pass, looked up and nonchalantly curled a 25-yarder beyond Kuszczak.
It was a fitting finale for Bergkamp. Arsenal had designated this as 'Dennis Bergkamp Day' for their fans. Many turned up in orange shirts to salute the Dutchman's 11-year contribution to the club and in that moment he rolled the years back.
For West Brom though, relegation rolls ever closer.