Alexandre Lacazette gave the Gunners the lead after 19 minutes, following in on a free-kick by Alexis Sanchez that hit the crossbar.
Lacazette claimed his brace after 67 minutes from the penalty spot as Aaron Ramsey was fouled by Allan Nyom.
The victory moves Arsenal up to seventh in the league standings.
Sanchez and Mohamed Elneny were drafted into manager Arsene Wenger's starting XI, as the Chilean superstar made his first start with Lacazette in the attack.
West Brom's Gareth Barry broke the Premier League all-time appearance record as he played his 633rd match.
Despite the hosts' dominance in possession, it was West Brom who should have taken the lead in the opening stages.
Jay Rodriguez was clearly brought down in the penalty area by Shkodran Mustafi, but the striker rose to his feet, prompting the referee to play a surprise advantage. The striker's shot clattered the post, with replays showing the faintest of touches from the glove of goalkeeper Petr Cech.
The Baggies were clearly miffed by the ref's decision not to award the penalty, and the Gunners took advantage as they grabbed the opener.
Sanchez's free-kick was accurate and true, but it hit the crossbar, bouncing down for Lacazette to finish.
The Frenchman has found an early knack of scoring at the Emirates, and there was never a doubt as he headed the ball home.
OptaJoe highlighted the strike:
Arsenal hunted a second before half-time, but the visitors remained dangerous as they tried to rob the Gunners on the counter-attack.
Hal Robson-Kanu and Rodriguez both had good opportunities to level the score, but Arsenal held on to their lead at the interval.
The hosts put their foot on the gas at the opening of the second half, and Lacazette should have doubled the advantage as he missed the target. Mustafi also went close with a deft flick from a corner, but West Brom remained alive in the match.
Arsenal finally made it 2-0 after 67 minutes as Ramsey was crudely brought down by Nyom. Lacazette took the ball and placed it on the spot, making no mistake as he slotted past stopper Ben Foster.
Bleacher Report's James McNicholas tipped his hat to the goalscorer:
The Baggies were fatigued and broken in the final 10 minutes, and Arsenal monopolised the ball as the visitors begged for the final whistle.
It was a simple win for the Gunners as their new striker was the hero of the hour.