Despite cruising the victory in the final stages of the match, the Gunners relaxed play was in stark contrast to a whirlwind first-half.
Albion should have opened the scoring after just eight minutes when they were wrongly denied a penalty for Shkodran Mustafi's challenge on Jay Rodriguez.
The Englishman decided to stay on his feet instead of going down and his subsequent strike was tipped onto the post by Petr Cech.
Lacazette then put Arsenal ahead on the 20 minute mark after being the first to react to Alexis Sanchez's free-kick crashing into the cross-bar.
Nacho Monreal saved a certain Baggies goal seven minutes before half-time when he cleared Grzegorz Krychowiak's header off the line.
The win takes Arsenal to 7th place on the Premier League table, while West Brom replace the Gunners in 12th place.