Burnley missed the chance to go back to the top of the table but a strong, disciplined display at the back kept their promotion charge on course.
Wimbledon showed few signs of breaking them down and looked a long way from a side with ambitions of making the play-offs.
This second goalless draw in five days at Selhurst Park offered little encouragement of them winning their FA Cup replay at Middlesbrough and earning a home tie with Manchester United.
Burnley came with a cautious approach, packing the midfield and leaving Ian Moore to battle on his own up front.
It was not entirely surprising as they had leaked five goals in their last away game at Manchester City.
Wimbledon had most of the possession but could make no headway in the first half hour as Burnley built a formidable barrier in front of goalkeeper Nikolaos Michopoulos.
It was only in the 15 minutes before half-time that Wimbledon began to see any signs of success from their patient probing.
A fine ball from Damien Francis gave Neil Shipperley half a chance but the striker stumbled as he span away from his marker.
David Connolly had the best chance of the half when a pass from Kevin Cooper gave him the opportunity to turn sharply in the box but his shot was hurried and high.
Half-time brought a welcome chance of heart by Burnley who introduced a second striker, the Greek Under-21 Dimitri Papadopoulos for midfielder Paul Cook.
The Greek's pace was soon in evidence as he raced onto a pass from Kevin Ball but Wimbledon goalkeeper Ian Feuer was able to clear.
The substitute's fourth appearance of the season was to be short-lived, however, as he was replaced himself by another attacker, Tony Ellis.
Wimbledon manager Terry Burton turned to winger Gareth Ainsworth with half an hour to go. Ainsworth came on for his first game of the season, replacing Joel McAnuff, after a nine-month absence through injury.
It was nearly a dramatic return but Ainsworth failed to connect properly with two half-chances in a goalmouth scramble.