There was little new year cheer for Martin Allen's boys as Lee Peacock's 31st minute strike put the Robins within a point of the Dons in the table, after McLeod had seen his 35th minute penalty saved and had a late goal disallowed.
The Dons dominated the first half but, after Jon-Paul McGovern, Lloyd Dyer and Aaron Wilbraham had missed good chances, Peacock put Swindon ahead against the run of play in the 31st minute.
The Dons' defence failed to clear Michael Timlin's dangerous inswinging corner and Peacock rammed in the loose ball from close range following a goalmouth scramble.
Wilbraham had an angled volley superbly saved by full-stretch Robins goalkeeper Phil Smith as the Dons pressed for an immediate response, before McLeod's 35th minute penalty misery.
McLeod's spot-kick was saved well by Swindon keeper Smith low to his right, after the quick Dons striker had been brought down in the box by Jerel Ifil.
Milton Keynes started the second half brightly but Christian Roberts smashed a dipping 25-yard free-kick just over the bar for the Robins, before Paul Butler's hooked 15-yard effort was cleared off the line by Swindon skipper Ady Williams at the other end in the 54th minute.
Dyer belted a 30-yard free-kick high over the bar and McLeod fired wide after turning Ifil on the edge of the box as the Dons' frustrations grew.
At the other end, Ricky Shakes missed a great chance to make it 2-0 when his stinging nine-yard angled drive was saved well by Dons goalkeeper Lee Harper in the 74th minute.
But as the Dons piled forward McLeod had a goal ruled out for offside a minute later after he had converted McGovern's spilled shot from close range.
And substitute Gareth Edds had a 12-yard strike deflected just wide and another effort blocked on the line by a wall of Robins' defenders in stoppage time as the MK Dons' club record winning run came to an end.