In the 2008/09 campaign, under the stewardship of Owen Coyle, the Clarets embarked on a League Cup run that gave birth to the tag "Capital Punishment".
The club had beaten Fulham, Chelsea and Arsenal before bowing out to Spurs in a two-legged semi-final in extra-time at Turf Moor.
But they weren't finished with London. Not by any stretch. A remarkable run in the Championship saw the Clarets break in to the top six where they would eventually reign supreme against Sheffield United in the play-off final at Wembley.
They went in to the Premier League feared by the clubs operating in the country's capital. However, that would be short-lived.
Since that day Burnley have played 13 games in London in the top flight and they haven't experienced victory in any of them.
This time Burnley were made to pay the penalty at the London Stadium as West Ham inflicted a sixth defeat on the road in the Premier League.
The Clarets were heading in to the interval level with the Hammers until Ben Mee gave Winston Reid a push in the box in first half stoppage time.
Goalkeeper Tom Heaton plunged low to his left hand post to keep Mark Noble's spot kick out but the skipper was quick to respond and guided the rebound home.
It was the fifth time this season that Sean Dyche's side had conceded in additional time; the third in the opening 45 minutes after allowing Leicester City and Bournemouth through.
The visitors hadn't really been in the game up until that point - it took them until the half hour mark to crank up the pressure - though the hosts hadn't asserted themselves on the fixture either despite bossing possession.
In the opening 10 minutes Andy Carroll headed wide from Michail Antonio's cross, Heaton saved from Dimitri Payet and Manuel Lanzini scooped over the bar.
And that set the tone for the remainder of the half. Slaven Bilic's men probed but were restricted to shots from distance.
Carroll failed to trouble Heaton soon after when moving goal-side of Mee from Payet's pass before the home side had, what appeared to be, a legitimate call for a penalty.
Reid's header from Payet's floated corner clearly struck the arm of Michael Keane but referee Bobby Madley was oblivious to the incident.
After Antonio drew another stop from Heaton, Pedro Obiang thumped the outside of the upright with a rasping drive as the Clarets failed to close the Spanish midfielder down.
United were dominant, working the ball on the outskirts of the penalty area, but they rarely exposed Burnley's backline as they struggled to craft a threatening opening.
Even French magician Payet failed to inspire as he skied an effort from the angle of the box having shaped the ball on to his right boot.
The home side did penetrate on one occasion with Payet slipping a pass in to Aaron Cresswell but the unmarked full back delayed his strike and Matt Lowton was able to get across to make a superb block.
With the clock ticking down, Noble went close when his measured curler came back off the post but the captain would get on the scoresheet before the break.
Heaton, with England boss Gareth Southgate watching on from the stands, attempted to beat Payet's set-piece away under pressure and as the ball fell for Reid the defender was knocked off balance by Mee.
Noble went to pass the ball in to the corner, Heaton saved, but as the ball spilled back in to the six-yard box the midfielder fired in to an empty net with the last kick of the half.
Burnley improved after the break and went close to an equaliser on a number of occasions but they weren't able to find a way through.
Mee almost made amends for his earlier error when heading Arfield's free-kick towards Sam Vokes inside the six-yard box but the striker failed to apply the vital touch.
Then, from a similar routine, with Keane applying the header on this occasion, the Welshman's improvised flick from close range drifted wide of the upright.
Vokes was certainly getting in good positions for the away side but he should have found the net with his next contribution.
After Darren Randolph saved from Arfield, and Cresswell cleared off the line under pressure from Andre Gray, the striker raced in to the box with the ball hanging in the air but headed over the bar with the goal gaping.
Randolph denied Arfield once more in the second half, adjusting his footing well to move to his left and beat the Canada international's free kick to safety.
Substitute Andre Ayew had a chance to double the Hammers' lead late on but, after breaking in to the penalty area, the forward guided his attempt narrowly wide of the far post.