Clive Platt's first-half double helped MK Dons secure a 2-1 win against Lincoln and set up an FA Cup second-round tie at Southend.
Platt's goals came either side of Paul Mayo's 24th-minute penalty, but the League Two side's woeful finishing cost them dear.
Gary Birch had already squandered a great chance for the Imps before the Dons took the lead in the 14th minute.
Nicky Rizzo's cross cleared a statuesque Lincoln defence and Platt controlled with his chest before lifting the ball over the advancing Alan Marriott for his fourth goal of the season.
But City levelled eight minutes later when referee Mike Jones penalised Craig Morgan for a tug on Marvin Robinson in the box and Mayo slammed home the spot-kick.
That gave the Imps the new belief but they fell behind again two minutes after the break. Trent McClenahan swung in a cross, Platt threw a knee at it, and Marriott could only watch as the ball looped in at the far post.
Birch missed another sitter on the hour, Mayo volleyed over and substitute Maheta Molango also went close, but the Dons held on.