James Constable and Peter Leven struck to bring the U's the reward of a home tie against League One high-flyers Sheffield United next month.
It is the first time Oxford have reached the third round since the 2002/03 season when they lost to Arsenal at Highbury.
This second-round replay, postponed because of a frozen pitch last Wednesday, took an age to get going and had nothing of the entertainment and excitement of the first match, a 3-3 thriller at the Crown Ground.
Accrington right-back Aristote Nsiala made two superb goal-line clearances within a few moments of each other from Constable and Tom Craddock.
Oxford stepped up their pressure in the second half but the breakthrough came from an Alfie Potter counter-attack after 66 minutes.
Potter's 50-yard run and shot by Constable forced a corner and from Leven's flag kick, Constable powered home a header.
Constable turned provider to set up Leven for a beautifully-hit left-foot volley from 20 yards 10 minutes from time.
The U's also had the boost of seeing veteran defender Michael Duberry come on as a sub after six months out with a neck injury.
