Reeves scored from the penalty spot and rounded off a free-flowing move with a fine finish in the first four minutes of the second half.
Corby reduced the arrears through Andre Johnson but Academy striker Sam Nombe restored the two-goal advantage in the final 15 minutes, completing a good evening’s work in muggy conditions.
Karl Robinson’s men looked sharp in possession from the first minute and they threatened soon after when Dean Lewington’s dangerous delivery had to be cleared away at the back post.
Two minutes later, Tom Hitchcock wasn’t able to quite get enough on George Williams’ teasing cross from the right as the Dons maintained their strong start.
Giorgio Rasulo then saw a shot blocked after more good build-up play before first-year professional Connor Furlong fired wide after a smart turn.
Corby’s first opportunity came on 25 minutes when Callum Ball curled an effort wide of the left-hand post following some nice footwork 15 yards out.
At the other end, Reeves forced Aidan Grant into two saves either side of some nice football involving Rasulo and Carruthers, who was denied by a good block.
The Dons deservedly took the lead on 47 minutes when Reeves picked himself up after being brought down in the box to smash the ball past Grant from 12 yards. 0-1.
Reeves doubled his and the Dons’ tally just two minutes later, sweeping home Rasulo’s cross from close range after a free-flowing move.
Corby, themselves, were awarded a penalty on 55 minutes after Joe Walsh handled in the area – substitute Andre Johnson made no mistake from the spot.
Hitchcock thought he had restored the Dons’ two-goal advantage but his effort was ruled out for offside midway through the second half.
George Baldock, Paul Downing, Ben Tilney, Daniel Powell and Sam Nombe were all introduced with 20 minutes remaining as Robinson aimed to continue to provide action to his squad.
Brandon Thomas-Asante was also introduced shortly afterwards and he made an immediate impact, forcing Grant into a save but the Corby keeper couldn’t keep out Nombe’s header as the Dons made it 3-1.
Powell almost made it 4-1 in the closing stages but he dragged his shot off target when well placed, this coming prior to a rasping shot from Tilney which flew just wide.
MK Dons: Burns; Williams (Baldock 71), Walsh (Downing 71), Jackson; Lewington (c) (Tilney 71); Carruthers (Kasumu 81), Upson (Powell 71); Furlong (Thomas-Asante 78), Reeves (Nombe 71), Rasulo; Hitchcock.
Goals: Reeves (47 & 49), Nombe (78).