A spectacular overhead kick from James Constable in the eighth minute was cancelled out by Rhys Murphy on the stroke of half time, before Dave Kitson's header in second-half injury time broke Dagenham hearts.
It was from Danny Rose's chip that United's leading scorer pounced, and did so in spectacular fashion. His perfectly executed acrobatic effort from 12 yards flew past the desperate dive of Lewington in the Dagenham goal.
The visitors mustered their first opportunity on target in the 30th minute when Zavon Hines' effort was easily dealt with by Ryan Clarke in the Oxford goal.
As half time loomed it was a clever piece of thinking from Murphy that drew his side level, the former Arsenal man chipping the ball over the stranded Clarke.
But in the dying seconds Kitson towered above the visitors' defence to power a header into the net to break Dagenham hearts.