West Brom's goal was the first Burnley have conceded at Turf Moor since 21 December
Burnley manager Scott Parker and defender CJ Egan-Riley were both sent off after the final whistle as West Brom put a dent in the Clarets' promotion hopes as they were held to a draw.
John Swift's excellent free kick - the first goal Burnley have conceded at Turf Moor since December 21 - put the Baggies ahead in the first half of a tight encounter which keeps Tony Mowbray's side in the hunt for a top-six placing.
The lead lasted just three minutes before Zian Flemming snapped up a fumble by West Brom keeper Joe Wildsmith to level for Burnley.
Both sides hit the bar in the second half, Jaidon Anthony for Burnley and Mikey Johnston for the Midlanders, before Parker and Egan-Riley were both shown red cards by referee Gavin Ward.
Egan-Riley was dismissed after he clashed with Baggies player Will Lankshear, who was shown a yellow card, and Parker was also punished for getting involved in the melee that followed.
Burnley later confirmed that they would appeal Egan-Riley's red card.
Mowbray had described his team's visit to Turf Moor, which has been something of a fortress all season, as a "free hit", and he made five changes to his line-up, with Darnell Furlong serving the first of his three-match ban.
The Baggies were certainly not passive against a Clarets side that went into the game having conceded just four in 18 home league games this season, and who possess the only unbeaten home record in the Championship.
The draw means they are now without an away win in their past 11 games, their worst run outside the top flight since 2000, but this felt like a positive.
Swift's opener was certainly a plus, as he cleverly moved the ball back a yard to improve his angle while referee Ward was making sure the defensive wall was a sufficient distance. Still, the way he curled the ball over that wall and into the top corner was top-class.
The lead lasted just three minutes as Lucas Pires cut in from the left flank and let fly. Wildsmith should have dealt with it easily enough but in trying to catch he dropped the ball and Flemming had the simple task of sidefooting it over the line.
Burnley pushed for another goal as Josh Brownhill's excellent cross just evaded Anthony and Egan-Riley's shot was well blocked by Isaac Price.
The Baggies had their own efforts, as Grady Diangana played in Adam Armstrong and the normally prolific Southampton loanee shot weakly at James Trafford.
The second half saw both sides unable to make the difference, although Anthony's curler bounced off the bar and Johnston also crashed a shot against the woodwork in the closing stages.
The game descended into chaos at the final whistle after Egan-Riley reacted to a little shove from Lankshear with a petulant hack at the West Brom man and was dismissed. Parker also saw red after remonstrating with the official over his decision.
Burnley first-team coach Mike Jackson:
"I think there's a lot of emotion.
"I think both teams are going for it, both teams are at different stages of where they need to be.
"The detail of it is not something that I want to try and get involved in because that much has gone on at the end but from what I've seen, I don't think there's a lot in it.
"I think sometimes we just need to take a little bit of a step back, everybody involved, but we'll look at it as a club."
West Brom manager Tony Mowbray told BBC Radio WM:
"Every point is important and that will be a good one if we get three on Saturday against Hull - hopefully we will have players back that we missed tonight.
"Since the day I walked in I've watched John Swift and with the ball he has got amazing, fast, clever feet, an amazing awareness of what is around him - in small-sided football you just can't get it off him. He's a wonderful talent.
"In really tough games like this we need to keep the ball away from the best teams because they are relentless on top of your goal.
"John helps us have periods in the game where we can dominate the ball, and with the talent he possesses he can stick it in the top corner."
