Leon Knight's predatory finish, Lloyd Dyer's close-range strike and skipper Keith Andrews' volley capped a dominant display from the Dons to demolish the Shrews.
Milton Keynes controlled the game from the off and Andrews' fierce 25-yard free-kick was beaten out by Shrews goalkeeper Glyn Garner in the 12th minute before Stuart Nicholson wasted the visitors' only chance of the half when he fired straight at MK keeper Willy Gueret from 15 yards five minutes later.
Andrews, Aaron Wilbraham and Mark Wright all went close before Knight put them ahead two minutes after the break.
The diminutive striker raced onto Andrews' flick and rammed home his third goal in as many games high past Garner from an acute angle.
Shrewsbury battled back and Dave Hibbert almost equalised when he fired against the crossbar from 12 yards before Nicholson was denied by a brave block from Gueret.
But Dyer doubled the Dons' lead in the 77th minute when he latched onto Knight's pass and finished well from six yards before Andrews volleyed home a poor defensive header from 14 yards to make it 3-0 five minutes from the end.
The Dons laid siege to the visitors' goal in the closing stages but Wright and Dean Lewington were both denied by Garner as the hosts cruised to victory.