Jeff Goulding came off the bench to grab an 87th-minute winner, in a thrilling game at the EBB stadium that ended 3-2, after the Shots threw away a two-goal lead.
Paul McCallum gave Aldershot a controversial lead when the linesman confirmed he had bundled Craig Reid's cross over the line despite Damien Batt's attempted clearance.
Reid doubled the lead from the spot but Scott Davis and Jon-Paul Pittman drew Oxford level either side of Michael Raynes' red card.
But the Shots hit back through Goulding to end a run of six games without a victory for the league's bottom club.
"We made it hard for ourselves but the way we responded was tremendous and we deserved to win the game. We are right back in the hunt," said Scott.
"It gives us a real boost. This is why we turn up - it's so people go home happy. The crowd got right behind us and lifted us.
"Four points over the weekend is a good return. Now we are starting to pick up the points we deserve and we have to go to Port Vale and put in another performance.
"We are in touch with a lot of teams now and that's brought us back to the pack.
"From what I've heard the first goal was clearly over the line and there wasn't much appeal from the Oxford players."