The victory sees West Brom move up to ninth to leapfrog Burnley, who remain four points clear of the relegation zone.
Matt Phillips struck after just four minutes at The Hawthorns after Dean Marney inadvertently rolled the ball into his path and even though the away side saw plenty of the ball, West Brom made it 2-0 soon after.
On 16 minutes Salomon Rondon set up James Morrison to shoot past Tom Heaton into the bottom corner after Burnley failed to close the midfielder down on the edge of the box.
Phillips went close again and Burnley seemed determined to press the self-destruct button, with England international Heaton gifting the ball to Morrison, but he sliced wide.
Heaton then redeemed himself to stop a Rondon curler that was destined for the top corner.
But the overworked goalkeeper had no chance on 37 minutes after Phillips and Morrison were again heavily involved, setting up former Manchester United midfielder Darren Fletcher at the back post to make it 3-0 and game over.
Venezuelan striker Rondon, who was a menace all night, finally got the goal he deserved when he swivelled in the box and let loose, the ball pinging off two Burnley players and into the net midway through the second half.
West Brom move up to ninth to leapfrog Burnley, who remain four points clear of the relegation zone.