Connor Roberts' 87th minute goal booked the Clarets' place in the Emirates FA Cup quarter-final with a 1-0 win against Fleetwood Town.
Burnley dominated the game throughout but it was the Welshman's second goal in successive games that secured the hosts' place in the last eight of the competition.
Manager Vincent Kompany made seven changes from the side that beat Huddersfield 4-0 on the weekend.
Bailey Peacock-Farrell came in for Arijanet Muric between the sticks, whilst Jordan Beyer kept his place in defence with Vitinho, Ameen Al-Dakhil and Charlie Taylor all coming in for Connor Roberts, Hjalmar Ekdal and Ian Maatsen.
Johann Berg Gudmundsson, Nathan Tella and Ashley Barnes all made way for Michael Obafemi, Lyle Foster and Scott Twine in attack.
First Half
The Clarets’ first real opportunity of the game came when Foster nicked the ball from the feet of Holgate on the halfway line, before racing towards goal and looking to dink the ball over Lynch only for the Cods ‘keeper to gather the ball to safety.
Burnley were dominating possession and Vitinho was next up to find the opening goal but the Brazilian’s effort from outside the box sailed well over the crossbar.
Midway through the first half, Taylor then lined up an effort from 25-yards out but the former Fleetwood loanee’s strike fizzed over Lynch’s goal.
Taylor then then tried his luck again minutes later with a low driven shot but Lynch was equal too it and was there to deny the full-back a first Clarets goal.
With half-an-hour on the clock Zaroury’s hooked attempt from the edge of the area was pushed wide by the hands of Lynch.
Fleetwood were then dealt a blow just before half time when Hayes clattered into Cullen and was shown a straight red card.
Second Half
The Clarets started the second 45 minutes on the front foot and came close to an early opener when Zaroury broke into the area and saw his strike ripple the side netting of the goal.
With 20 minutes to go Taylor then had the best chance of the game when his header from close range was blocked on the line by Holgate.
Foster then had a glorious chance to sweep the ball low past Lynch after being played through on goal in the area but the South African's effort fizzed across the face of goal.
With the clock ticking down in the final 10 minutes, Al-Dakhil then went for goal from 30-yards out but the defender's shot was hit well over the crossbar.
But with just two minutes left on the clock, following a goalmouth scramble Roberts was there to turn it home from close range and seal Burnley's place in the quarter-final.
Burnley will face Manchester City in the FA Cup Quarter Final, with the game due to be played the weekend of Saturday 18th March. Tickets will go on sale on Monday 6th March, more detailed information will follow.
Burnley: Peacock-Farrell, Vitinho, Al-Dakhil, Beyer (Roberts 62), Taylor, Cullen, Brownhill © (Gudmundsson 62), Twine, Foster (Dervişoğlu 84), Obafemi (Tella 62), Zaroury (Churlinov 73)
Unused Subs: Muric, Sassi, Bastien, Barnes
Fleetwood Town: Lynch, Vela ©, Holgate, Andrew, Warrington, Robertson (Gomes 66), Macadam (Batty 66), Hayes, Nsiala, Earl, Rooney
Unused Subs: Cragg, Johnson, Patterson, Johnson, McMillan, Lane, Sarpong-Wiredu
Goals: Roberts 87'