New Dons' Spanish goalkeeper Adolfo Baines, signed on a free transfer from Tenerife in the summer, saw red just 37 minutes into his debut for handling outside the box.
But McLeod rose to the challenge and stroked home a penalty and then rammed in a sizzling 83rd minute winner after Andy Bishop had replied for the Shakers.
The Dons started brightly and Clive Platt headed Jon-Paul McGovern's cross just over the bar under pressure from Bury skipper Dave Challinor.
Bury threatened in the 25th minute when Andy Bishop latched on to Marc Goodfellow's precise lofted through ball, but his attempted lob from an acute angle was comfortably gathered by Dons' keeper Baines.
But the Dons continued to dominate, and Jon-Paul McGovern's cheeky angled lob from the edge of the box hit the bar two minutes later with Bury keeper Alan Fettis well beaten.
After surviving that scare, Bury hit the woodwork themselves when Bishop raced on to Goodfellow's through ball and fired against the post under pressure from Dean Lewington just after the half hour mark.
Dons' chances were dealt a blow in the 37th minute when Baines was sent off for handling outside his area as Bishop looked to latch on to Goodfellow's long pass.
Flitcroft stung Dons' substitute keeper Ademola Bankole's hands minutes after the re-start when he cut in from the right and fired in a powerful 18-drive shot.
McGovern's 51st minute free-kick was deflected just over the bar off the Bury wall.
McLeod gave the Dons a 59th minute lead from the penalty spot after Platt had been brought down by Bury keeper Fettis.
Bishop looked to have earned the Shakers a point when he coolly slotted home an 80th minute penalty on his debut after he was pulled down in the box by Drissa Diallo.
But McLeod charged down John Fitzgerald's clearance before smashing a terrific half-volley inside the near post seven minutes from the end to get Allen's reign off to a dream start.