On-loan Fulham goalkeeper Bettinelli pulled off some superb saves in the second half as United hunted for the winner.
Stanley started well with winger Kal Naismith's early shot flying just wide while Oxford had to defend numerous Lee Naylor free-kicks.
Naismith came close again with a superb solo effort when he went on a mazy run into the area but was denied by the outstretched foot of Oxford 'keeper Ryan Clarke
United's first-half chances were limited, with David Hunt's free-kick always going over while Bettinelli palmed away James Constable's close-range header just before half-time.
However, the visitors, unbeaten away from home this term, upped their game after the break with wide man Sean Rigg firing into the side-netting while Dave Kitson skimmed his header just wide of a post.
Then it was the Bettinelli show as he denied Kitson after 70 minutes with a superb save from a close-range header.
The Stanley stopper then kept out Rigg's fierce drive and one-handedly pushed away Michael Rayne's low header.
Stanley finished strongly and almost grabbed the winner themselves in injury time but Peter Murphy was unable to turn the ball into the net amid a frantic goalmouth scramble and both sides had to settle for a point.