A first-half strike from Tim Cahill and a goal late on for the returning Louis Saha saw off Tony Mowbray's battling side, who simply didn't hit the target enough.
A bright start from the visitors saw James Morrison taking early control of the ball and running at the Everton back-line, feeding frontmen Jay Simpson and Marc-Antoine Fortune but efforts from both in the first five minutes lacked power and rolled kindly to Tim Howard in goal.
The Blues struggled to keep hold of the ball and were quickly pressured by swarms of yellow jerseys but a quick break from Steven Pienaar created space for Leighton Baines to float a high cross to Tim Cahill at the back post but his header flew way over the bar.
West Brom still looked threatening and a dangerous corner was only half-cleared off the penalty spot by Cahill's head and an onrushing Robert Koren smashed his shot a yard wide of the post.
The game was continuing at a frantic pace with both sides having chances at either end but Everton came the closest so far after Cahill put the ball in the net but referee Steve Bennett ruled that the Aussie had climbed on Baggies captain Paul Robinson.
Mowbray's side were not playing like a team rooted to the bottom of the table and a defence-splitting ball from Borja Valero on the half-hour mark left Fortune with only Howard to beat but the keeper showed why he has only conceded three times in ten games and quickly got off his line to block the shot from close range.
Everton started throwing men into the box looking for the opener and, despite being dominated for most of the half, a well-floated free-kick from Baines found an unmarked Cahill to break the deadlock on 36 minutes.
With no Mikel Arteta taking precedence over free-kicks it was Baines who whipped in the high cross and a piece of terrible marking from Gianni Zuiverloon left Cahill free to set himself and power home his eighth of the season.
Unlucky to be a goal down West Brom came out after the break desperate to find an early equaliser and a long-range drive from Valero flew just wide of a scrambling Howard in goal.
The visitors should have equalised just before the hour mark after a deep corner from Chris Brunt gave substitute Luke Moore his first touch of the ball with a towering header at the back post.
Moore's looping effort flew over Howard and a mass of players and was heading for the bottom corner before Everton's player of the season, Phil Jagielka, showed exactly why he is in the England squad with a superb block on the line.
With Marouane Fellaini still not match fit and picking up his 12th booking of the season, Blues boss David Moyes replaced his £15million man with striker Saha who has just returned to the first team himself.
The move proved to be a stroke of genius by Moyes as the Frenchman latched onto a Steven Pienaar interception and, after taking a touch to turn inside his man, unleashed a vicious curling shot from outside the box which gave Scott Carson no chance and put the game well out of the reach of the Baggies.
West Brom almost bagged themselves a consolation in the final minutes after a 25-yard thunderbolt from Moore clattered against the bar but Everton never looked troubled by West Brom who struggled to hit the target with their numerous chances.