Daniel Powell opened the scoring after just 50 seconds but Drogs captain Lloyd Buckely levelled things up before half-time with a tap-in.
Powell, though, restored the lead with a 25-yard strike before Brandon Thomas-Asante secured the triumph with his second goal in as many games.
The XI that started Monday’s victory over St. James’s Gate were selected to start the first 60 minutes, with the intention to give the other group half an hour at the end of the game - this will be reversed on Wednesday, in the Dons’ final friendly.
On Monday it took the Dons nine minutes to break the deadlock but after just 50 seconds in County Louth, Karl Robinson’s men found themselves ahead courtesy of Powell’s first goal of the summer.
The winger, who will be looking to return to his 2014/15 form this season, finished off a slick team move which involved Ben Reeves and second-year scholar Hugo Logan - the latter grabbing the direct assist. 0-1.
The dozen or so Dons fans in attendance were in jubilant mood after the early goal but their adulation quickly to turned to laughter as a local rabbit made its way across the United Park pitch with the game in full flow.
Meanwhile, the men from MK1 continued to assert their dominance on the Drogs and they almost doubled their lead in the 15th minute when Powell picked out Lewington with a cross. The skipper brought the ball under control but his shot was parried over by Patrick Dunican.
The man in the opposite full-back position to Lewington, George Williams, then went close with a header from Reeves’ corner which just skimmed the crossbar on it’s way over.
Robinson’s side threatened to add to their tally again on 22 minutes when Lewington connected with a corner from the left, however the skipper couldn’t direct his header on target.
It felt as though there was only a matter of time before the Dons found a second goal and in someways, on 35 minutes, they did, although Powell’s neat finish was ruled out for offside by the linesman.
The Drogs never really looked like threatening the scoreline early on but with nine minutes remaining in the first half they found themselves an equaliser with their first real effort on goal - a tap-in from their captain Buckley after Burns could only parry Gareth McCaffrey’s driven free-kick. 1-1.
Sam Nombe almost found an immediate response with a deflected shot but he and his team weren’t able to restore their lead before half-time.
At the break, Robinson made one change to his side with Oran Jackson replacing 16-year-old David Kasumu in the centre of defence and the second-year scholar was called into action early on to deal with a threatening attack.
It didn’t take long, though, for the Dons to re-establish their control on the game and 11 minutes into the half, Reeves came close to scoring from a second free-kick in as many games but this one was gobbled up Dunican.
Then, just as Robinson readied his 10 changes, Powell collected the ball in the middle of the park and unleashed a low, driven shot into the bottom left corner, doubling his tally for the evening and put his side back in front. 1-2.
Those 10 planned substitutions were then made by the manager but they soon had the only player to remain on the pitch, Charlie Burns, to thank for keeping the scores as they were after he pulled off a decent save to deny Drogheda substitute Paul Finnegan.
The change in line-up didn't affect the Dons’ dominance over their opponents and Samir Carruthers almost added a terrific third goal five minutes after coming on, but his curling effort just went wide.
Maynard was then denied his second goal of the summer on 70 minutes by a superb point-blank save by keeper Dunican, who then watched as the striker headed wide a cross from Carruthers.
Later, Connor Furlong produced a save out of the Drogs stopper before coming close to picking out Brandon Thomas-Asante with a teasing cross.
Thomas-Asante went into the game on the back of a fine strike in the 9-1 win over St. James’s Gate and with four minutes remaining he bagged the Dons’ third and final goal with a neat one-on-one finish after terrific work from Hitchcock to create the chance.
Two wins out of two then for the Dons, who play a behind-closed-doors friendly on Wednesday before flying back to the UK.
Starting XI: Burns; Williams (Baldock 60), Kasumu (Jackson 46), Walsh (Downing 60), Lewington (Tilney 60); Upson (Potter 60), Rasulo (Carruthers (60); Logan (Furlong 60), Reeves (Hitchcock 60), Powell (Thomas-Asante 60); Nombe (Maynard 60).
Subs not used: Martin.
Goal: Powell (1, 59), Thomas-Asante (84)