Albion's summer signing scored his third goal of pre-season (55) to cancel out Thanasis Karagounis' first-half strike (11), and further goals from Saido Berahino (75) and Markus Rosenberg (87) gave the Premier League side victory.
The game was hosted by Shrewsbury owing to ongoing work at The Hawthorns, and Steve Clarke's side fell behind when Karagounis finished off a quick counter-attack from the Greek visitors moments after Shane Long had missed at the other end.
Referee Stuart Attwell turned down a couple of Atromitos penalty appeals, while the lively Berahino tested Italian goalkeeper Luigi Cennamo after wriggling free in the box.
Anelka was introduced at the break and took just 10 minutes to head his side level from Billy Jones' cross, and the goal was the spark Albion needed to go on and dominate.
Teenager Berahino had already hit the bar by the time he converted Rosenberg's cross, and provider then turned scorer as the Sweden striker netted from 20 yards with the help of a deflection.