Karl Robinson’s men made the majority of the running in their second friendly in as many days but they were unable to find a way past the Irish Premier Division side’s dogged defence, and were then caught on the counter-attack with four minutes to go.
Dele Alli came the closest to scoring for the men from MK1 with a penalty which was expertly saved, while Danny Green saw a curling 20-yard free-kick hit the woodwork.
Robinson made just one change from the side which started the 6-0 success over St James’s Gate, with David Martin replacing Ian McLoughlin as part of the goalkeeper rotation.
Dean Lewington fired over a free-kick in a first 20 minutes which saw Drogheda make it very difficult for the Dons.
The skipper then turned provider shortly afterwards with a perfectly-waited pass for Tom Hitchcock, who was brought down in the box by the hosts’ keeper Dylan Connolly, but Dele Alli saw his resulting spot-kick smartly saved.
David Martin was called into action for the first time on 29 minutes, denying Declan O’Brien from close range after he was picked out by fine pass from a team-mate.
At the other end, a clever chest down by Giorgio Rasulo presented Dean Bowditch with a shooting chance, but his 20-yard effort was comfortably gathered by Connolly.
This was followed by chances for both sides 10 minutes before the break, with Gavin Brennan not able to quite connect with Peter McGlynn’s dangerous cross for the hosts and Mark Randall shooting straight at Connolly from 25 yards for the Dons.
Daniel Powell was the first to register an effort eight minutes into the second period, sending a shot narrowly past the right-hand post after a powerful run at the heart of the Drogheda defence.
Kyle McFadzean ensured the score remained level with a fine block to thwart O’Brien as the hosts tried to catch the Dons on the counter-attack, before he, Martin, Tom Flanagan, Lewington, George Baldock, Bowditch, Rasulo and Hitchcock were replaced by McLoughlin, Antony Kay, trialist Jay McEveley, Gedeon Okito, Danny Green, Will Summerfield and Kabongo Tshimanga on the hour mark.
McLoughlin made a routine save from Carl Walshe before Darren Potter was introduced for Alli 11 minutes later. Fellow substitute Green then hit the woodwork with a curling 25-yard free-kick prior to Powell firing wide after nice link-up play with Tshimanga.
Robinson introduced Ben Tilney and Kyran Wiltshire for Randall and Powell late with just under 10 minutes left, but neither of them could do anything to stop Walshe driving home from inside the Dons’ box on 86 minutes.
There was still time for Summerfield to see a shot squirm past the right-hand post after good work on the left by Tilney.
Despite the result, it was another productive friendly for the Dons as they faced a step up in opposition.
Starting XI: Martin (McLoughlin 61), Baldock (Hodson 61), Lewington (Okito 61), McFadzean (Kay 61), Flanagan (McEveley 61), Randall (Wiltshire 82), Alli (Potter 71), Powell (Tilney 82), Bowditch (Green 61), Rasulo (Summerfield 61), Hitchcock (Tshimanga 61).
Subs not used: Hickford.