Hal Robson-Kanu scored and was then sent off as the Clarets were once again unable to find a way past West Bromwich Albion.
The Baggies have never lost a Premier League game at Turf Moor.
And after two previous draws, Tony Pulis’ side went one better with a first away win of 2017 on an afternoon of frustration for the Clarets.
Both sides had started with opening-day wins as Burnley looked to make it two in a row at the start of a top-flight season for the first time since 1973.
But it was the Baggies who re-wrote their history books as they ended a 39-year wait to kick off with back-to-back victories at this level thanks to Robson Kanu.
The striker had been on the pitch for only seven minutes when he punished Burnley’s sole defensive lapse of the afternoon to break through and bag the winner.
Thirteen minutes later he was then sent off for a challenge on Matt Lowton but the Clarets were unable to hand out further punishment as they were unable to repeat their first-half fluency or make a late onslaught count.
Not surprisingly, the Clarets started with an un-named starting line-up from the side that began the season with a bang by beating champions Chelsea at Stamford Bridge on the opening day.
That meant an attacking midfield role for Jeff Hendrick in support of Sam Vokes and it was Hendrick who had the Clarets’ first two attempts in a slow burner of an opening half.
The Ireland international shot wide after being teed up by Jack Cork and then saw another effort charged down after a Robbie Brady corner had dropped at his feet.
It was the Clarets who carried the greater threat as they stepped up the momentum ahead of the break on the back of some carefully controlled football, Johann Berg Gudmundsson popping up either side of the half-hour mark with a curling effort just past the post and a header saved by Ben Foster from a Robbie Brady cross.
Brady’s delivery looked a likely route to goal as he then crossed for Sam Vokes at the end of the best move of the first 45 minutes, launched by Cork’s typically excellent run from deep.
Vokes got goal-side of Ahmed Hegazi, but couldn’t get enough on his header to add to his opening-day brace.
Eight years ago to the day, Foster had been beaten by Robbie Blake’s memorable winning goal against Manchester United to launch the Clarets’ first Premier League campaign.
But the England international didn’t need to pick the ball out of the same net in front of the away supporters as he survived one more scare a minute before half-time as Ben Mee steered a header inches wide at full stretch from another Brady corner.
Predictably, the Baggies’ biggest goal threat had also come from set-pieces, although Sam Field knew nothing of the effort he headed over the top when looking to avoid a 40th-minute corner from Chris Brunt on Brunt’s 500th club appearance.
The visitors – with former Burnley striker Jay Rodriguez closely shackled and starved of meaningful service – were never in a hurry to do anything but prevented the Clarets from getting a clear sight of goal.
Even a Brady free-kick from inches outside the penalty area couldn’t beat a wall of blue and white shirts after an hour.
And the Clarets’ frustration was compounded when West Brom then grabbed the winner with their first effort on goal 20 minutes from the end.
There appeared little danger when Brunt hooked a hopeful ball forward but Matt Phillips got a decisive touch to the dropping ball to allow Robson-Kanu to burst through the Clarets’ suddenly-stretched defence and steer a shot past Tom Heaton.
Dyche responded by sending on Jonathan Walters and Ashley Barnes to try and create a fresh angle to the Clarets’ attack.
And Burnley were faced with 10 men for the closing stages after Robson-Kanu was sent off.
The Wales international led with an arm as he jumped towards Lowton, although any contact with the defender’s face looked to be accidental.
That forced the visitors even further on the defensive and to take even more time out of the game.
But with the clock against them, the Clarets finally found a head of steam and almost saved a deserved point with a late flurry of chances.
Hendrick clipped an effort over the top before Vokes flashed a header over the bar from a Steven Defour cross.
And with almost the last touch, Walters just failed to locate the top corner as he nodded a Hendrick cross wide of the target as the Clarets were forced to stomach a repeat of last season's loss first time up at Turf Moor.
The rest, as they say, was history.
Burnley: Heaton, Lowton, Tarkowski, Mee, Ward, Gudmundsson (Barnes 78), Defour, Cork, Brady (Walters 78), Hendrick, Vokes. Substitutes: Pope, Long, Taylor, Westwood, Arfield.
West Bromwich Albion: Foster, Nyrom, Dawson, Hegazi, Brunt, Phillips, Livermore, Barry, Field (Rondon 84), McClean (Robson-Kanu 63), Rodriguez. Substitutes: Myhill, Chadli, Harper, Leko, Wilson.