Walsall, unbeaten on the road in their previous six, gradually grew into the contest and almost took the lead with their first attempt on 27 minutes.
Josh Ginnelly’s corner found the run of Laird, whose stooping header looked goalbound until it hit Ed Upson in the six-yard box, with the ball eventually being cleared.
The Dons’ reprieve proved short-lived, though, as the same two players combined again barely a minute later - this time to devastating effect.
Ginnelly received possession out on the right and delivered an accurate far-post cross to Laird who powered a bullet header beyond home keeper David Martin.
The visitors were controlling proceedings and they threatened to extend their lead before the break, Erhun Oztumer trading passes with Simeon Jackson before firing over from 25 yards.
Half-time: MK Dons 0-1 Walsall
MK Dons made a purposeful start to the second-half, with Colclough unleashing a powerful 18-yard strike which Neil Etheridge beated away to his right.
The hosts went close again on 52 minutes, as Dean Bowditch’s downward header from Colclough’s cross bounced down into the ground and came back off the post.
Walsall – looking to make it six unbeaten in League One – soon regained control and had chances to put the game to bed.
Dons custodian Martin made a smart reaction save to parry Ginnelly’s deflected set-piece, and Oztumer curled narrowly wide after intercepting Samir Carruthers’ misplaced pass.
Then, a slick Saddlers move culminated in Oztumer crossing low for Jackson, but he was unable to get enough on it.
On 69 minutes, Walsall had a golden opportunity to kill the game off. Ginnelly found McCarthy on the overlap and the Southampton loanee accurately cut the ball back for Oztumer, who side-footed inches wide of the far post.
Jon Whitney’s men were almost made to pay for their profligacy moments later, but Etheridge produced a fine full-stretch stop to turn away Reeves’ well-struck 30-yard drive.
The danger wasn’t yet averted and from the resulting corner, Jack Hendry’s header was cleared off the line by Joe Edwards.
The home side continued to press for an equaliser, with Colclough’s deflected shot on the turn being acrobatically tipped over by Etheridge.
And the pressure told in the final minute of normal time, as Bowditch brought the ball down in the area and curled a precise left-footed effort into the bottom corner.
Full-time: MK Dons 1-1 Walsall
Team: Etheridge, McCarthy, Toner, Preston, Laird, Chambers, Edwards, Ginnelly (Osbourne 84’), Moussa, Oztumer, Jackson (Bakayoko 76’).
Subs not used: MacGillivray, O’Connor, Dobson, Sangha, Cockerill-Mollett.