The Baggies looked set to end Burnley's proud unbeaten home record this season after Darnell Furlong's early opener but the hosts hit back twice in the final 15 minutes to win, deservedly on the balance of play.
We rated Carlos Corberan's squad from a disappointing finale in Lancashire as Albion remained sixth in the Championship after spending much of the evening up in third place.
Alex Palmer 7
Not too many big saves for the the keeper to make – but did what he had to do when called upon. Produced a superb reaction save in the first half to divert an Erik Pieters deflection onto the post and keep Albion in front.
Darnell Furlong 7
Did superbly well to get on the end of a Swift cross and head home. Involved in a flashpoint was Nathan Tella went down in the box, but replays showed it was not a penalty. Hard to get forward as Burnley pressed but did his job well.
Erik Pieters 6
Back at his old club, it was a busy night for him and O'Shea. Headed absolutely everything for the majority of the evening and kept the Burnley front line quiet despite pressure. However, the goal came down his side as Tella ran clear and he'll be disappointed in that.
Dara O'Shea 7
Good display from the Irishman. Like Pieters headed everything, put his body on the line like all Albion players did and did not concede many clear cut chances to Burnley.
Conor Townsend 6
Did a solid job defensively having to come up against Burnley's tricky wide players. One thing that Townsend and Albion as a whole struggled with was getting forward out wide. Didn't have the same joy he did against Luton.
Okay Yokuslu 7
In a tough game like this, the Turk is even more of a joy to watch. So dominant in the middle on a tough night against quality opposition. Got stuck in to win ball back when he could. Albion missed his presence while receiving treatment for Clarets equaliser.
Jayson Molumby 7
Yet another storming performance from the terrier-like midfielder who is enjoying some fine form at the moment. Particularly in the first half, he was Albion's best player and absolutely relentless in his running and tackling.
Grady Diangana 6
He was the stand-in for the injured Phillips and, following a bright start, both Diangana and Albion as an attacking force began to wane. Showed some effort but level of confidence and belief not where his side need it.
John Swift 7
Deployed unusually out on the left early on and something of a menace for the hosts to pick up in a floating role. Excellent set-pieces helped create opener. Used it well in general but tired later on and was withdrawn.
Jed Wallace 6
The usual hard running from Albion's flying winger – who began in a No.10 role to accommodate Diangana – and some dangerous moments early on but again his impact dropped as Burnley took grip of game. One who kept running until the bitter end.
Daryl Dike 6
Something of a slow start in this one and struggled to get going and recover from that. Looked a yard of pace short, no lack of effort but did not come off for the big striker. He looked exhausted in the second half.
Tom Rogic (for Swift, 67) 5
Unable to have the impact he or the head coach would have hoped. Not strong enough when battling for some balls.
Adam Reach (for Diangana, 83) n/a
Might his fresh legs and busy style have been useful earlier for Albion?
Karlan Grant (for Molumby, 88) n/a
Desperate roll of the dice from Corberan after Twine fires free-kick winner.