Hull were quick out of the blocks on a snow-coated pitch and Danny Allsopp should have given them the lead just 40 seconds in, but fired wide from eight yards after Robbie Stockdale's cross caused panic in the Dons' defence.
Milton Keynes fought back and Paul Mitchell clipped a free-kick just over the angle in the 13th minute, after Leon Cort's foul on the edge of the box.
Allsopp came close again for the visitors eight minutes later, turning Leon Crooks in the box before fizzing a drive just past the far post.
At the other end, Wade Small's fierce half-volley from 15 yards flew just wide on the half-hour mark after Hull's Roland Edge blocked his first effort.
The Dons' Izale McLeod dragged his left-foot shot wide of the post when well placed five minutes before the break.
And then the Tigers' Facey somehow screwed his shot out for a throw-in after Michel Pensee-Bilong's slip gave him a clear sight of goal just ten yards out.
Hull were made to pay for that miss when Lewington put the home side ahead five minutes after the re-start.
The lively McLeod raced away down the left and when his cross was volleyed back across the face of goal by Small, Lewington was on hand to tap his second of the season past Boaz Myhill from four yards.
Facey almost equalised a minute later, but his effort from just inside the box was deflected agonisingly past Matt Baker's post.
McLeod and Lewington both came close to extending the Dons' lead, before Facey took advantage of some slack marking to notch the equaliser from close range in the 86th minute.