Belgium internationals Romelu Lukaku and Kevin Mirallas struck the decisive blows for Roberto Martinez's side, with Albion contributing to their own downfall at The Hawthorns.
Jonas Olsson gifted the ball to Lukaku for the opening goal of the game in the second minute and Ben Foster somehow allowed a shot from Mirallas to sneak under his body midway through the second half.
West Brom showed plenty of endeavour in trying to get back into the game but demonstrated a lack of composure in front of goal as they slipped to a second league defeat of the season.
Saido Berahino and Craig Gardner had their best openings but both lashed efforts over the crossbar, with Tim Howard rarely forced into a save.
The win moves Everton into the top half of the table at this early stage of the season while Albion, who have only won four home league matches in the last 12 months, occupy the relegation zone.
With only two minutes played winless Albion showed their fragility as Olsson handed Everton the initiative after failing to deal with a poor cross from Leighton Baines.
The England international's delivery eluded any blue shirts in the penalty area, but Olsson scuffed his clearance straight to Lukaku and he finished emphatically from 18 yards with a curling effort.
Alan Irvine's side, who were without Stephane Sessegnon with an eye injury, responded well to going behind but were unable to test Tim Howard in the Everton goal, Berahino going closest as he lashed a 12th-minute effort over the crossbar.
The hosts continued to pose more of an attacking threat up until the break but suffered from a lack of quality in the final third.
On several occasions the final ball into the penalty was easily cleared by the visitors and when chances did present themselves they were wasted by Berahino and Brown Ideye.
West Brom's attacking momentum continued in the second half but it was Everton who went closest to the game's second goal.
After leaving Olsson on the floor Lukaku stretched Ben Foster with a low shot, the England goalkeeper parried the ball into the path of Steven Naismith but he blazed over from six yards.
Everton's second goal of the game came in the 66th minute as another mistake from Albion allowed Mirallas to score.
Having jinked away from the Albion defence the 26-year-old fired towards the bottom corner but, rather than making a regulation save, the ball squirmed under the body of Foster and into the back of the net.
Aiden McGeady could have extended Everton's advantage with 17 minutes to play but the forward was unable to repeat his midweek goal for the Republic of Ireland as he fired wide.
Berahino and substitute Georgios Samaras finally tested Howard in stoppage time with shots in quick succession but the American was up to the challenge and preserved his clean sheet.
