Goalkeeper Adam Legzdins scored a dramatic injury-time equaliser to extend the Clarets’ unbeaten start to the season in remarkable style.
Two first-half Palace goals looked set to hand Burnley their first defeat of the campaign at the 15th time of asking and leaving them with just one point from their opening two group games in the Premier League Cup.
But after Ali Koiki had pulled a goal back with his ninth of the season, Legzdins came forward for a last-gasp corner and nodded home the equaliser with virtually the last touch of the game.
It was the first goal of the goalkeeper’s career and a fitting reward for another determined fightback from the U23s.
The side currently being looked after by Andy Farrell don’t know when they are beaten as they came from behind for a fifth game in a row to record an incredible 11th draw of the season – including the result at Middlesbrough which got their cup campaign up-and-running.
That looked unlikely when the Eagles led by two goals with more than an hour gone.
Palace have been on a poor run of five successive defeats – including a loss to Blackburn Rovers in their opening Group G tie.
But they struck twice within the space of five minutes in a game switched from Bamber Bridge to Barnfield because of a waterlogged pitch at the Sir Tom Finney Stadium.
The weather barely relented at the Clarets’ training ground either and the home side was taking on water when Rob Street slotted home on the break and Brando Aveiro doubled Palace’s lead with an explosive strike into the roof of the net.
Burnley had seen plenty of the ball but the nearest they came to a reply was an effort from Joe McGlynn (above) bravely blocked by goalkeeper Ollie Webber just before the break after Tunde Bayode had squared for the teenage striker.
Chances remained scare in the second half, despite Burnley dominating possession.
But the Clarets kept plugging away and after Lewis Richardson had gone close, top scorer Koiki came up with the goods again when he crashed home a superb volley from Josh Benson’s corner with 23 minutes to go.
Richardson then went close to an equaliser when his flick from a Joel Mumbongo cross was saved.
And deep into injury time the Clarets’ pressure finally paid off in the most unlikely of circumstances.
Legzdins had been a big part of last season’s run to the quarter-finals and the experienced keeper - featuring as an over-age player - came up trumps again in less conventional style.
With only seconds remaining, Legzdins joined the last attack and from Benson’s in-swinging corner he nodded the ball home to complete a great escape and keep the unbeaten run going.
Burnley: Legzdins, Cooney, Koiki, Benson, Wilson, Glennon, Bayode, N’Guessan (Phillips 62), Harker (Richardson 45), McGlynn (Mumbongo 67), Tucker. Substitutes: McMahon, Cropper.
Crystal Palace: Webber, Boateng, Daly, Boateng, Rich-Baghuelou, Mensah, Pierrick (Lokilo 60), Steele, Street, McGregor, Aviero (Williams 87). Substitute: Henry, Chamberlin-Gayle, Gordon.
Referee: Lewis Smith