Milton Keynes-born Brooker seized upon a defensive error to bag his 13th goal of the season in the fourth minute, extending the Robins' unbeaten run to five games.
Dons manager Danny Wilson made one change to the team that beat Bradford 2-1 just under two weeks ago, with Ben Chorley replacing David Partridge, as the centre-half was not allowed to play as he is on loan from Bristol City.
Robins boss Gary Johnson named the same team that drew 1-1 with Nottingham Forest last Saturday.
Milton Keynes started brightly but a horrible error by Chorley gifted Brooker the opener for City on the counter-attack in the fourth minute.
Chorley let a routine long ball slip under his boot and skipper Brooker burst clean through to fire low across Dons goalkeeper Ricardo Batista and into the bottom corner.
The lively Brooker forced Batista into a decent low save with a fizzing strike from the edge of the box before Scott Murray fired a dipping angled drive just over midway through the first half, as the Robins searched for a second goal.
Dons defender Trent McClenahan's heroic lunging block prevented Bas Savage converting from five yards, before Murray rounded keeper Batista by the corner flag only to see his effort from an acute angle cleared off the line by Chorley in the 27th minute.
And as the Dons continued to ride their luck, Bradley Orr's 25-yard thunderbolt was saved at full stretch by Batista just after the half-hour mark.
Three minutes before the break Dons substitute Paul Mitchell was booked, even though he wasn't on the pitch, for holding back the furious Savage on the touchline. The City man also received a yellow card.
Savage warmed Batista's hands with a low strike from the edge of the box as the visitors burst out of the blocks in the second half.
At the other end, McClenahan's swerving 25-yard strike almost wrong-footed Robins keeper Adriano Basso, but he just recovered in time.
Gareth Edds tested Basso again a minute later from long range as the Dons upped their game, before the Robins' shot-stopper tipped substitute Nicky Rizzo's 30-yard free-kick around the post in the 66th minute.
City defender Louis Carey was lucky to escape with just a booking for hauling down Izale McLeod as he burst through two minutes later.
Murray went close for the Robins at the other end in the 70th minute with a sweetly struck half-volley that was clawed out of the top corner by Batista.
But the Dons continued to press and after Ben Harding's 20-yard half-volley had come back off the inside of the post, substitute Clive Platt's close-range follow-up was miraculously turned over the bar by Basso, as the visitors hung on.