The France striker – who has scored in each of those home wins – headed into an open net in the 20th minute after West Brom goalkeeper Ben Foster tipped Alexis Sanchez’s free-kick onto the crossbar.
West Brom felt they should have been awarded a penalty before the opener when Shkodran Mustafi brought down Jay Rodriguez with a sliding challenge – but no foul was given by referee Bobby Madley.
Instead of staying on the ground following the contact, Rodriguez chose to continue but his shot was tipped onto the post by a diving Petr Cech.
After the break, Arsenal were themselves rightly awarded a spot-kick when Allan Nyom barged over Aaron Ramsey close to the byeline.
Lacazette stepped up and calmly slotted into the bottom right corner – his fourth goal since his club record £46.5m summer move from Lyon.
The Baggies caused Arsenal problems in the first half in particular, with Nacho Monreal brilliantly clearing a Rodriguez header off the line in the 38th minute.
Victory for the Gunners lifts them to seventh in the table, one point behind fourth-placed Tottenham and six behind leaders Manchester City.
West Brom – on the night midfielder Gareth Barry broke the Premier League appearance record – drop to 12th.
