Dons midfielder Darren Potter deflected Andy Taylor’s free-kick past his own goalkeeper after just four minutes as the hosts were struck an early blow.
And Bradshaw secured Walsall all three points when he struck twice in the second half to silence Stadium:mk, with the hosts slipping from second to fourth in the table.
MK Dons had scored 13 goals in their previous two home league games, but were left stunned within two minutes when the Saddlers took a shock lead as Taylor’s mis-fired free-kick cannoned off Potter’s shin and into an empty net.
Bradshaw should have doubled the Saddlers’ lead just before the break when put through one-on-one with goalkeeper David Martin, but his low left-footed shot was superbly pushed wide for a corner.
But Welsh international Bradshaw struck his 13th goal of the season just after the hour-mark when he intercepted a Dons back-pass, ran round the on-rushing Martin and tapped home into an empty net.
Bradshaw then celebrated his 14th in the 77th minute when he slotted home after Martin could only push Romaine Sawyer’s shot into his path.