In a game of few chances Oxford goalkeeper Jamie Ashdown acrobatically kept out a Rigg volley on the half hour.
After the break neither side created any meaningful chances, Rigg denied a winner by the offside flag in the 86th minute meaning the home side have now gone four games without a win.
Danny Hylton went close for the visitors after just three minutes but from then on it was all Wimbledon as Adebayo Akinfenwa went close twice and Ashdwon kept out Rigg’s volley on the half hour.
But Kemar Roofe almost made the hosts pay for their profligacy, firing a stinging shot just wide of James Shea’s far post after good work down the right wing from United just before half-time.
After the break Adedeji Oshilaja was stretchered off and taken straight to the ambulance after he landed badly on his head when jumping high for a header.
And the game somewhat petered out, with Rigg’s late disallowed goal the closest either side came to a winner despite 11 minutes of injury time.