Centre-back Mullins, signed from Rotherham, finished what looked like a well rehearsed routine as he turned in David Hunt's free-kick in the 80th minute.
Danny Rose fired the U's in front after 33 minutes with a superb free-kick, curling a 25-yard shot over the wall and just inside goalkeeper Rob Lainton's left-hand post. The brilliant skills of home winger Alfie Potter lit up the first half.
Potter excelled on the pristine Kassam Stadium pitch, which was relaid in the summer, producing two outstanding runs past three opponents.
But Bury pressed hard in the second half and when Craig Jones darted into the box and crossed in the 70th minute, Tom Soares converted with a shot high into the roof of the net.
To cap the Shakers' unhappy day they had Nathan Cameron sent off for a second yellow card in the 83rd minute.
That came just moments after he was cautioned for the foul which brought Oxford the free-kick for their winning goal.