Dagenham started the first half with real intent and were clearly not overawed by the former League team.
In the first minute an early first-time cross from Glen Southam just evaded the onrushing Cliff Akurang.
Three minutes later the Daggers broke through again with some excellent interplay down the left hand side. Scott Griffiths played a neat wall pass with David Rainford and found Akurang. The Ghana-born striker failed to keep his header under the bar from five yards.
On nine minutes Griffiths found himself some space again picking up a clearance from an initial cross from Sam Sloma. His instinctive cross shot from 20 yards just crept over the bar.
Griffiths found himself in the same position from a Sloma pass in the 19th minute. This time he elected to take it on the volley from the edge of the penalty area. The drive was swerving into the far corner and would have been the opener, but for an excellent diving save from Billy Turley.
The sustained pressure on the Oxford goal was starting to tell and two minutes after Griffiths let fly, the U's found themselves a man down.
Rainford beautifully carved open the Oxford defence with a 30-yard through ball. Barry Quinn was caught flat footed as Paul Benson raced clear. Unable to recover he hauled him down on the edge of the area.
Referee Cann had no hesitation in pulling out his red card in the 21st minute. The resulting free-kick came to nothing.
Sam Saunders should have deservedly put the Daggers in front on 32 minutes. He turned the opposition defence inside out on the edge of the area but dragged his shot from eight yards. Turley got down easily to make the save.
The U's were clearly struggling to come to terms with the nitty gritty of Conference football. Andrew Burgess drove from similar range to his goal at the weekend, but otherwise failed to trouble Tony Roberts.
Their only other chance came on the 38th minute, Matthew Day found the otherwise anonymous Ed Hutchinson, his flick fell to Rob Duffy, but his header from close range failed to trouble Roberts.
Oxford's first-half performance forced Jim Smith to change his line up at half-time. Yemi Odubade came on for Burgess and Christian Hargreaves replaced Hutchinson.
Initially the changes had little effect, Phil Gilchrist found himself making a last-ditch challenge on Benson, if not perfectly timed it would have ended in the same result as Quinn's red card.
Danny Foster then hit the bar on 50 minutes with Turley well beaten. Returning to the Dagenham side from injury, Foster mistimed his cross but gave the Oxford defence an almighty scare.
However, the pace of Odubade was beginning to tell. Ten minutes in a desperate challenge from Anwar Uddin denied the striker on the edge of the area.
Oxford then broke through against the run of play a minute later, the Dagenham defence did not reorganise from the resulting throw-in.
Day found Duffy inside the box, his mis-cued strike fell to Odubade, who reacted brilliantly to drive low into the bottom corner.
The Daggers responded well to the setback. Rainford struck beautifully from 30 yards. The drive appeared to be heading into the top corner until Turley managed to claw it over the bar.
On 70 minutes they appeared to get the breakthrough they deserved, Akurang showed great skill to break into the box, but failed to pull the trigger with his left foot with a goal at his mercy from seven yards.
In the final minute Sloma flashed in a great cross and Akurang, with his last chance, could only find the goalkeeper with a header from close range.