Substitute Chris McCann's late winner dented 10-man West Brom's Coca-Cola Championship play-off hopes.
Goals from Jason Koumas and Nathan Ellington saw the visitors race into a two-goal lead with just seven minutes on the clock.
But, with Andy Gray having closed the gap with a quarter of an hour gone, West Brom's Paul McShane was sent off just before the interval.
The Irish defender challenged for a header but only connected with Burnley's James O'Connor and his dismissal by referee Mike Jones provoked fierce protests from Baggies boss Tony Mowbray at half time.
Gray took just two minutes of the second half to get the Clarets back on level terms with a close-range finish to take his tally to 13 for the season.
The visitors looked like they would hold on for a draw but McCann's 87th-minute header means they stay fifth, with just a one-point cushion over the chasing pack.
That all looked very unlikely when the Baggies got off to the best possible start thanks to some trademark magic from Wales international Koumas.
The midfielder skipped past Eric Djemba-Djemba and O'Connor in central midfield to allow him the space to shoot from 25 yards.
Goalkeeper Brian Jensen got a hand to the ball but could not keep it out.
Just over a minute later, the lead was doubled when Ellington headed in off his own hand from Zoltan Gera's cross, with Clarets defender Wayne Thomas in close attendance.
The Clarets were initially rattled but pulled one back in the 15th minute.
Baggies goalkeeper Dean Kiely's poor throw caught Jonathan Greening napping and Mike Duff's block tackle fell kindly for Gray, who, despite a suspicion of offside, tucked the ball away from the edge of the box.
After the excitement of the goals, the game settled into a scrappy tussle with little in the way of flowing football.
Koumas tried another from long range in the 30th minute but Jensen palmed away the Welshman's half-volley.
A Koumas free-kick was then headed wide by Gera as the visitors pressed for a third.
On the stroke of half-time, McShane was shown a straight red card for his aerial challenge on O'Connor.
While there was concern for O'Connor, who had to be carried off on a stretcher, there was no sign of malice in McShane's challenge.
Just two minutes after the restart, the hosts were level.
Wade Elliott's corner to the far post was met by Thomas and Gray bundled in from close-range.
McCann then robbed Diomansy Kamara in midfield and fed Ade Akinbiyi but the striker produced a weak shot that failed to trouble Kiely.
Elliott's header also lacked power but Kiely pulled off a fine stop in the 62nd minute from McCann's thumping header.
McCann's fierce drive flew just high and wide a couple of minutes later and Steven Caldwell headed over.
With just over three minutes left, the impressive McCann headed the winner from Duff's deep cross to earn Burnley a fifth win in six matches.
Teams:
Burnley Jensen, Duff, Thomas, Caldwell, Harley,Elliott (Spicer 79), James O'Connor (McCann 45), Djemba-Djemba,Jones, Akinbiyi (McVeigh 72), Gray.
Subs Not Used: Coyne, Coughlan.
Booked: Djemba-Djemba, Harley, Elliott.
Goals: Gray 15, 48, McCann 87.
West Brom Kiely, Albrechtsen, Perry, McShane, Robinson,Greening, Koumas, Koren, Gera, Kamara (Phillips 76),Ellington (Chaplow 64).
Subs Not Used: Daniels, Hartson, Hodgkiss.
Sent Off: McShane (45).
Booked: Kamara, Gera.
Goals: Koumas 6, Ellington 8.
Att: 12,500
Ref: M Jones (Cheshire).