Wimbledon came from two goals down to end an eight-match losing run in their first game at Milton Keynes' National Hockey Stadium.
Wimbledon's first game in Milton Keynes drew a crowd of over 5,000
Dean Holdsworth began the Dons' comeback in the 66th minute and Patrick Agyemang snatched a point for Division One's basement side four minutes later.
Bereft of fans for over a year after their traditional support abandoned them over the relocation, 5,639 turned up at
Milton Keynes, including the visitors.
The kick-off was delayed by 15 minutes due to crowd congestion, and once the referee finally got play underway, the Dons made the worst possible start in their new home.
They conceded the softest of openers when Robbie Blake's 25-yard free-kick took a cruel deflection off the wall before bouncing agonisingly past goalkeeper Paul Heald.
An unmarked Blake then made it two in the 37th minute, finishing a Delroy Facey cross with a shot which deflected in off unfortunate Dons defender Rob Gier.
But the Dons were handed a lifeline when Clarets defender David May was sent off after a deliberate handball on 58 minutes, having already been booked for a first-half foul on Nigel Reo-Coker.
Holdsworth then got them right back in it with his second goal of the season, converting Agyemang's low cross in the 66th minute.
Provider then turned goalscorer when Agyemang headed his fifth of the season from Jobi McAnuff's cross in the 71st minute.
Wimbledon: Heald, Holloway, Leigertwood, Gier, Darlington,
Nowland, McAnuff, Reo-Coker, Jarrett, Holdsworth, Agyemang.
Subs: Banks, Gray, Chorley, Gordon, Kamara.
Burnley: Jensen, West, May, Todd, Camara, Farrelly, Weller,
Blake, Chadwick, Ian Moore, Facey. Subs: Roche, Branch, Grant,
Referee: M Warren (W Midlands)