West Brom delivered the archetypal smash and grab act at Turf Moor, scoring the only goal with their only real effort of note.
Substitute Hal Robson-Kanu settled the issue 20 minutes from time, in a game where Burnley dominated throughout, without being able to break down an obdurate Baggies defence.
Burnley bossed the first half, patiently passing and probing, but couldn't work Ben Foster sufficiently.
Defending the goal he conceded Burnley's first ever Premier League goal at - to Robbie Blake eight years ago on that famous night against Manchester United - he only made one save of note, to deny a Johann Berg Gudmundsson header from a Robbie Brady cross just after the half hour.
The Clarets played on the front foot throughout, with good fluidity of movement, continuing to show better ball retention as the side evolves under Sean Dyche.
They had plenty of chances, as Jeff Hendrick, sporting a new shorter haircut, skidded a shot just wide from Jack Cork’s pass, while Gudmundsson was agonisingly close with a curler after Sam Vokes headed down a raking pass from James Tarkowski.
Vokes and Ben Mee also threatened with headers just before the break, as the sides went in goalless.
After the break, Chris Brunt wasted a free kick just to the right of the area, curling his effort over the angle, and Burnley continued to search for a way through.
Steven Defour’s half volley hits Hendrick and flew wide, and Brady drags a shot wide, before hitting the wall with a free kick on the edge of the area.
But with 20 minutes remaining, Matt Phillips beat Mee to flick on, and Robson-Kanu held off Tarkowski and beat Tom Heaton at the near post.
The Wales striker saw red seven minutes from time, somewhat harshly, after catching Matt Lowton with an arm, but West Brom held on to win, with substitute Jon Walters sending a free header over in injury time.