The U's also stretched their unbeaten run to 10 games in all competitions thanks to Peter Leven's 16th-minute spot-kick after Tom Craddock had his heels clipped by Sido Jombati as he raced into the box.
Robins boss Mark Yates felt it was "a soft penalty" but Wilder did not agree that it was a controversial decision.
"People go on about so-called bigger clubs in all the divisions getting decisions but we don't get anything from referees at home," he said.
"Leven stuck the penalty away nicely into the corner and that just gave us the edge.
"We should possibly have gone on and got a second goal but we ground it out and that's not something we've always been able to do here at the Kassam Stadium.
"It's been a fantastic effort from us to get nine points out of nine over Christmas. We've got to chase these teams, like Cheltenham, down.
"We've had two proper away performances with good wins at Exeter and AFC Wimbledon and then to get a result in a tight game against a good team sets us up nicely for some big games ahead."