It was a gritty win in the promotion clash at stadium:mk with the midfielder's 20th-minute header earning a smash-and-grab win.
It was Millwall's fourth straight away win and blows the race for second place wide open as they ended the Dons' eight-game unbeaten run.
Dons' challenge for second place is now looking in jeopardy after losing a game they couldn't really afford to.
Before the game Roberto Di Matteo had said it was a massive game and the celebrations of vociferous travelling Lions fans seemed to prove that.
Dons were on top throughout the first half and should have taken the lead after ten minutes. Dean Lewington's hoof upfield put Lions skipper Tony Craig under pressure as Jason Puncheon chased him down before bullying him off the ball.
He side-stepped keeper David Forde but the defender then did enough to put him off as he rolled his right-foot shot wide of the near post.
A minute later Puncheon then played Luke Chadwick through on goal but, with the target gaping, his angled drive went straight at Forde who palmed the shot away.
It cost the Dons as the visitors took the lead soon after. Referees must just not like the look of Miguel Llera as he was harshly judged to have pushed over Gary Alexander on the edge of the box.
From the resulting James Henry free-kick, Laird ghosted in at the near post unmarked and glanced the ball home superbly with his head.
It hit Dons and it took them a while to get going again. They did put the ball in the net as Puncheon swivelled and volleyed home Jemal Johnson's cross but he was offside.
After some intense pressure late on in the half, Millwall held on until the break.
A second-half onslaught was expected but it never really came. The ever imperious Puncheon had an early dribble and shot that went straight at the keeper.
They continued to huff and puff but found chances hard to come by, Alan Navarro was pushed on the edge of the box by Laird but from the resulting free-kick Puncheon floated a shot harmlessly over the bar.
The addition of Ali Gerba did little to inspire Dons into action either. With nine minutes left Dons fans thought another substitute had found that elusive goal as Daniel Powell rippled the net after a loose ball broke for him from a corner.
Unbelievably he hit the support behind the goal and the ball then cannoned into the net behind the goal.
With seven minutes left Dons surely should have had a penalty when Scott Barron was all over Wilbraham like a rash but the referee ignored the desperate pleas of the Cowshed.
The woeful Gerba then hit two ridiculous efforts from long range that didn't trouble Forde whatsoever.
Dons had a few late corners with Llera having a header cleared away by a wall of legs but it just wasn't to be.