Robbie Threlfall's superb inswinging corner drifted over U's keeper Luke McCormick and Redshaw headed powerfully home at the far post.
Oxford looked to be heading for a win that would have kept alive their faint hopes of reaching the play-offs. Alfie Potter fired in an angled shot on the hour mark from Sean Rigg's pass, though goalkeeper Barry Roche will be disappointed with himself that he could not do more to keep the effort out.
In the first half there was a lack of confidence in the Oxford team having lost their last two and on a pitch that made passing and control difficult.
Tom Craddock had an early opportunity to chip Roche but curled his effort wide. And when Potter was presented with a free header from Damian Batt's right-wing cross, he failed to get enough on it and saw the ball drift across the box.
Stewart Drummond had a similar free header for Morecambe from a corner at the end of the first half but saw it blocked on the line.
The U's stepped up the tempo after the break but Craddock blazed over from Batt's pass, with Batt probably better placed to have had a shot himself.
Kevin Ellison went close for the Shrimps late on with a 20-yard shot on the turn that just cleared the bar before Redshaw pounced in injury time.