Newly-crowned WBA World Heavyweight Champion and Millwall fan David Haye watched on as Neil Harris set the Lions on their way shortly after half-time before Price struck with his first touch.
Lewis Taylor got one back for the Dons before Danny Schofield extended the advantage and Price delivered the knock-out blow two minutes from time.
Haye was presented to the crowd at half-time and within three minutes of the re-start Steve Morison collected Brett Johnson's defensive header and chipped the ball to Harris who smashed home his 128th Millwall goal.
In the 71st minute the visitors failed to clear Nadjim Abdou's free-kick and Price stabbed the ball home before Taylor's 80th-minute strike from 12 yards gave the visitors hope.
But Schofield cut inside from the right and smashed home from 16 yards before Price finished off a flowing counter-attack in the 88th minute to send Haye home happy.