The Valiants had Chris Lines sent off for violent conduct in the first half, ruining the match as a spectacle, but the Dons moved themselves up to fourth in League One.
They went ahead in just the third minute when Baker took aim from the edge of the penalty area and shot low across Chris Neal and into the bottom corner.
Having barely seen any of the ball, Vale’s task was not made any easier after 37 minutes when Lines was shown a red card for head-butting Dele Alli.
Benik Afobe headed a wonderful chance for the Dons wide at half-time and Neal saved from Daniel Powell, who got a flick to Antony Kay’s effort.
MK Dons were unable to make the game safe against their depleted opponents thanks to some wayward shooting but the result was never really threatened.
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