Karl Robinson's side, who won automatic promotion behind Bristol City in May, fired three goals in the first 35 minutes to take control at New York Stadium.
Rob Hall's fifth-minute opener was cancelled out by Rotherham striker Matt Derbyshire, but Danny Collins' 28th-minute own goal and Dean Bowditch's close-range finish gave the Dons a 3-1 half-time lead.
Carl Baker drilled in a fourth for the Dons in the 75th minute.
In the lunch-time kick-off at Elland Road, Burnley substitute Sam Vokes' fine 86th-minute header rescued a point for his side in a 1-1 draw against Leeds.
Burnley, among the promotion favourites following relegation in May, were given a tough test by Uwe Rosler's side, who looked to have secured victory when Mirco Antenucci stepped off the bench to curl home a superb effort in the 83rd minute.
QPR also found it tough going following relegation to the second tier as they slipped to a 2-0 defeat at London rivals Charlton.
Addicks striker Tony Watt broke the derby deadlock in the 52nd minute and defender Morgan Fox added a second in the 72nd minute.
Hull fared much better in their first game back in the Championship thanks to goals from summer signings Sam Clucas and Chuba Akpom in a 2-0 home win against Huddersfield.
Clucas, a summer signing from Chesterfield, followed up the rebound from his own shot to score 39 minutes into his debut and Akpom, on a season-long loan from Arsenal, fired home the second in the 72nd minute.
Promotion contenders Derby were held to a goalless draw at Bolton where both sides were denied by the woodwork.
Derby's Johnny Russell's 26th-minute shot hit the crossbar and Bolton's Emile Heskey, Gary Madine and Darren Pratley all headed against the same bar in the second half
Home midfielder Jay Searing was sent off for a second yellow card late on.
Brentford struck twice in stoppage time to snatch a point in a thrilling 2-2 home draw against Ipswich.
Kevin Bru gave Ipswich an interval lead and summer signing Ryan Fraser put the visitors 2-0 up in the 50th minute, but Brentford striker Andre Gray struck in the second minute of time added on and James Tarkowski headed home four minutes later.
David Cotterill's 40th-minute free-kick and Arsenal loanee Jon Toral's debut goal seven minutes later helped Birmingham secure a 2-1 home win against Reading, for whom Orlando Sa missed a penalty in the eighth minute of stoppage time
Nick Blackman had earlier pulled one back for Reading in the 58th minute.
Goals from Benik Afobe and Dave Edwards clinched Wolves a 2-1 win at Blackburn, who replied through Craig Conway's emphatic 39th-minute finish
Sheffield Wednesday head coach Carlos Carvalhal made a winning start to life in England as his side secured a 2-0 home win against newly-promoted Bristol City
Defender Tom Lees headed home in the 60th minute and Lewis McGugan added a second in his first game since signing a permanent contract at Hillsborough 11 minutes later
Substitute Craig Noone produced a stunning late strike to earn Cardiff a 1-1 draw in the other lunch-time kick-off at home against Fulham
Matt Smith had given Fulham the lead two minutes into the second half when he pounced on a mistake by Cardiff goalkeeper Simon Moore
Source : PA