The former Leyton Orient striker made Dale's equaliser with a superb piece of skill and cross which Ernie Cooksey headed in seconds from the half-time break.
The draw helped prevent Oxford from doing the double over Steve Parkin's team, whose winless run now stretches to six games.
Angry Oxford fans protesting at chairman Firoz Kassam for the way the club has plunged since he took over were left frustrated because he wasn't at the ground at the start.
And when some unfurled a large "Kassam Out" banner, it was quickly taken down by stewards.
Oxford had two players making their debuts, centre forward Tim Sills from Aldershot, and 16-year-old Ben Weedon, who was tried on the left of midfield.
Brian Talbot's men passed the ball around neatly at times, belying their lack of confidence after losing six of their previous seven home matches.
A slick move by the home team ended with U's skipper Chris Hargreaves seeing his deflected shot saved. But it was Dale who had the first real opening when midfielder Neil Brisco burst past Oxford's centre-backs and had only keeper Chris Tardif to beat, but scooped his shot over.
Andy Burgess forced a save from Matthew Gilks with a curling effort from 20 yards before Ashton opened the scoring on 17 minutes. He challenged with two Rochdale defenders for the ball in the air at a corner and when it dropped he lashed a right-footed shot into the top right of the goal from 12 yards.
Cooksey flicked a header wide as Parkin's men looked for a response, but it wasn't until first-half injury time that they drew level.
Christie beat United's offside trap then roasted Leo Roget ands hung up a deep cross which Cooksey met with a header back across Tardif and into the net.
Dale had to reshuffle in the second half after defender Mark Jackson was stretchered off with a suspected broken leg.
Christie remained the most dangerous player on the pitch, and after he had gone close with an angled drive which flew over the bar, he had a goal ruled out for offside.
Steve Basham went close to a second-half winner for Oxford with a brilliant left-footed volley from 22 yards which Gilks just managed to turn around his post.