Raynes headed home in the 94th minute, seconds after Lee Molyneux had put Stanley ahead with a superb 20-yard free kick in the 91st minute at the Crown Ground on Saturday.
Stanley had the better of the early chances with striker Padraig Amond having a chance cleared off the goalline and Romuald Boco heading against the crossbar, but Oxford made a chance count when Jon-Paul Pittman tricked his way down the left, got the better of defender Toto Nsiala, drew goalkeeper Paul Rachubka and fired into the net after 12 minutes.
Stanley equalised after 25 minutes when Boco's cross from the left found Amond at the far post. He scuffed his effort, but the ball fell for Craig Lindfield to power home.
Pittman was lively up front for United, but fell heavily on the stroke of half-time and was stretchered off with a suspected shoulder injury and minutes after the restart Andy Whing went down on the edge of his own area and was also stretchered off with Oxford having used all three substitutes just after the break.
The game came to life with 10 minutes to go when James Beattie scored a wonder goal from 30 yards, hitting it first time into the top of the net. It looked like that would be the winner until James Constable fired low into the bottom corner with four minutes left before substitute Molyneux fired home a 20-yard free-kick and Raynes' dramatic equaliser.