The Youth Team crashed out of the FA Youth Cup, losing on penalties to the Metropolitan Police.
Khius Metz put the Clarets ahead midway through the first half and they looked to be in control of the tie.
But a shock equaliser from Luke Brant from the penalty spot sent the game to extra-time.
Josh Dolling’s 98th minute strike put Burnley back ahead, before a dramatic 120th minute equaliser from Ben Marret sent the game the distance.
It was a very bright start from the Clarets, with the hosts bombarding the Mets Police’s goal in the opening half an hour with several efforts before the opener.
Goalkeeper Callum Lunn kept the Clarets at bay after just two minutes, wonderfully clawing over a Tinashe Chakwana volley from an Andy Nugent free-kick.
The resulting Aiden O’Neill corner brought on Burnley’s next chance, but captain Shaun Hobson failed to find the target, narrowly heading over the angle.
Metz was a nuisance for the Met throughout the first half, and striker found Tyler Shrimpton at the edge of the box and a fine solo run, but the winger scoffed his strike, before the visitors finally cleared.
Lunn was then called upon again in the 10th minute, backtracking before superbly tipping over a deflected Dolling strike.
O’Neill, a second year scholar, who is a regular for the U21s played the duration of the cup tie, and the midfielder came close 10 minutes later.
Great feet allowed the Australian space before his low shot was routinely saved by Lunn.
But the Clarets finally broke the deadlock 20 minutes before the break.
A superb Shrimpton cross found Metz on the penalty spot, and the Ireland youth international controlled before lethally half-volleying past Lunn, who was finally beaten.
The visitors almost grabbed a shock equaliser when Lemar Fowakes’ cross-cum-shot was well parried to safety by Tony Aghayere.
Shrimpton found Metz once more on the stroke of half time with another delicious cross, but this time, the striker couldn’t double his or Burnley’s tally.
There was a reaction from the visitors after the break as the Met Police forced a good save out of the patient Aghayere.
Luke Robertson’s half volley from the edge of the box looked destined for the top left corner, but Aghayere was alert to collect.
The Clarets had to deal with relentless pressure from the visitors, with Burnley finding it hard to keep possession.
Dolling’s long-range strike whistled past the bottom left post, before the Met Police grabbed a shock equaliser.
Lewis Norvock brought down Tane Caubo in the box, allowing Brant to convert the resulting spot kick which squirmed under Aghayere.
In the final minute there was a final chance for the Clarets as Dolling’s flick-on for Tommy Wood was fired inches wide before Mark Howarth’s volley was bent wide with the final kick to send the game to extra time.
Lunn, who had a quiet start compared to the first, pulled off two stunning point blank saves, denying Dolling on both occasions.
But just two minutes later Dolling made amends, putting the Clarets back ahead in the cup tie.
Howarth beautifully threaded in the former Trafford loanee, who stabbed home past the onrushing Lunn.
Straight from the restart in the final period of the game, Dolling then turned provider when some skill beat fullback Brant before squaring to Miles Fenton, who again forced another fine save out of Lunn.
With just seven minutes remaining the visitors caused a late scare when Connor Gales’ header was wonderfully tipped onto the crossbar by Aghayere before the Clarets cleared.
But in stoppage time in extra time, the visitors grabbed the dramatic equaliser.
A long free-kick forward into a packed Burnley area was deep to the far post, where Marret glanced under Aghayere.
The shoot-out went to sudden death, and with Chris Ogunlana missing, Hobson needed to score to send Burnley through.
Another stunning save from Lunn again clasped the win away from Burnley, and with a miss from Howarth, the visitors progressed.
Penalty Running Order:
Burnley: Aghayere; Dixon, Hobson, Norvock, Nugent; Chakwana (Fenton 84), O’Neill, El-Fitouri (Howarth 62), Shrimpton; Metz (Wood 65), Dolling
Subs: Bruce, Grogan
Goals: Metz 27’, Dolling 98’
Met Police: Lunn; Ogunlana, Hancock, Gales, Brant; Pearn (Brown 110), Fowakes (Marret 67), Robertson, Scantlebury, Chislett (Green 58); Caubo
Subs: Opoku, Greenleaf, Willett, Taylor, Dicks
Goals: Brant 78’