Nick Pope kept a clean sheet to help the Clarets book their place in the semi-finals of the Lancashire FA Senior Cup.
Pope completed his third game since returning from a five-month injury absence as he continued to build up his match sharpness.
And while the England international was rarely tested, his assured handling and commanding of his penalty area underlined his well-being as Burnley set up a last-four trip to either Everton or Rochdale – who are scheduled to meet on Tuesday.
Stephen Ward also completed 90 minutes and Steven Defour played for 70 as the pair – who recently returned to action alongside Pope in the Clarets’ FA Cup win over Barnsley – benefited from a competitive run-out at the Barnfield Training Centre.
Fleetwood had reached the final in the each of the last two seasons, but any hopes they had of lifting the trophy at the third attempt disappeared with a 33rd minute own-goal from defender Cian Bolger.
Bolger (below) diverted a ball into the penalty area from Josh Benson – superbly found by Ward’s diagonal pass – past goalkeeper Billy Crenin to break the deadlock.
And while the Clarets were unable to their tally, they never looked like being pegged back in a game they dominated to get back to winning ways following back-to-back defeats in the U23 Professional Development League.
The ever-ready Defour set the tempo as he helped Steve Stone’s side dominate possession before the break, without making the most of a number of inviting positions.
Clear-cut chances remained elusive in the second half as the Clarets – who had beaten Barrow in the previous round – failed to press home their advantage.
Tunde Bayode fired an effort just wide and Ward wasn’t far off target with a well-struck effort from long-range.
Rob Harker did flick one effort goalwards and Harker and Dan Agyei were unable to meet a low cross from substitute Tinashe Chakwana late on.
But there were few alarms at the other end as Pope came to claim a couple of high balls into the penalty area to nullify any threat and ensure the Clarets’ smooth passage through.
Burnley: Pope, Cropper, Thomas (Cook 61), Glennon, Ward, Bayode, Defour (Howarth 76), Benson, Blair (Chakwana 82), Harker, Agyei. Substitutes: Bruce, Rain.
Fleetwood Town: Crellin, Holgate, Baines, Mashigo (Johnson 71), Bolger, Hill, Jones, Metete (Makepeace 84), Garner, Mooney, Clarke (Boyle 71). Substitutes: Clayton, Goldsbrough.
Referee: Conor Brown