The victory puts them within three points of the play-off places but for a long time it looked extremely unlikely as the Boro seemed destined to lift themselves out of the relegation zone.
Stevenage were in complete control at half-time after Dean Parrett's well-taken opener was added to by Lucas Akins penalty after Antony Kay bundled over Curtis Obeng.
But it was game on with 10 minutes left as Jordan Spence forced the ball in from close range after Chris Day had done brilliantly to keep out Lewington's header.
Ben Reeves then sensationally brought MK Dons level four minutes later as his wonderful strike from 30 yards flew into the top corner giving Day absolutely no chance.
And the comeback was complete four minutes into added time as the Dons captain Lewington rose to head Reeves' corner into the top corner.