Second-half goals from skipper Keith Andrews, Sean O'Hanlon and substitute Jude Stirling sealed the Dons' fourth straight win after David Brown had given lowly Accrington a half-time lead.
But in the end the result mattered little as Swindon's draw with Walsall condemned Milton Keynes boss Allen to his third successive play-offs.
Brown exposed the Dons' early defensive jitters to coolly put Accrington ahead in the 14th minute, stroking in Robert Grant's pass from 22 yards.
Paul Mullin almost made it 2-0 when he fired against the post three minutes before the break after racing clear onto Jay Harris' pass, before Gareth Edds saw his ferocious drive blocked on the goal-line at the other end by Stanley full-back Leam Richardson on the stroke of half-time.
Accrington keeper David Martin produced a string of fine saves to hold his old team at bay before Andrews equalised from the penalty spot in the 55th minute, after Izale McLeod had been tripped in the box by Richardson.
O'Hanlon then put the hosts 2-1 up with a towering far-post header from substitute Jon-Paul McGovern's free-kick in the 69th minute.
McGovern then chipped against the post from 25 yards before Edds somehow fluffed the follow-up against the upright from two yards.
But substitute Stirling's far-post header from Jon Hayes' corner sealed the win for the Dons in the 83rd minute.
The Dons will now face Shrewsbury Town in the play-off semi-finals.