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.
Blue Square Bet Premier sides Barrow and Macclesfield will replay to decide who makes the third round after Richie Baker missed a fine late chance to win it for the hosts.
On-loan Fleetwood man Kieran Charnock put the Silkmen ahead after 19 minutes but former Bury midfielder Baker levelled matters for the hosts 10 minutes later.
Both sides knew a money-spinning tie with Championship leaders Cardiff awaited the winners but Baker missed the best chance to decide it when he fired over with 15 minutes left.
Macclesfield went ahead when Charnock followed up Chris Holroyd's 20-yard free-kick and stabbed home after the returning Danny Hurst failed to gather.
Barrow nearly struck back, with lone striker Adam Boyes smashing a superb effort against Lance Cronin's post and away to safety after 26 minutes.
Barrow levelled three minutes later when Baker grabbed his ninth of the season as Cronin could only palm his curled 25-yard free-kick into the net.
Ex-Everton man John Paul Kissock struck Barrow's crossbar with 20 minutes to go, connecting on the volley from eight yards after Cronin fumbled.
Baker should have put the Bluebirds ahead but somehow steered Sean McConville's centre over the bar from five yards.
Rampant Rotherham booked their place in the third round after overcoming 10-man Notts County 3-0 at Meadow Lane.
The League Two side took the lead after nine minutes when winger Ben Pringle planted a superb 25-yard strike into the top corner.
Rotherham doubled their advantage against their sluggish hosts after 22 minutes when a Pringle corner wasn't dealt with and Mark Bradley swept the ball home.
It went from bad to worse for County on the half hour when defender Damion Stewart was adjudged by referee Darren Deadman to have deliberately elbowed Alex Revell and was handed a straight red card.
It was 3-0 in the 41st minute as Lee Frecklington broke away from the County backline and rounded keeper Liam Mitchell before putting the ball on a plate for Daniel Nardiello to finish.
A half-time triple substitution did little to liven the home side up and Nardiello missed a glorious chance to extend the away side's lead but the three first-half strikes proved to be enough.
Brentford moved into the third round with a 4-2 extra-time win over Bradford.
The Londoners will feel justice was done following Bradford's shock reprieve, after twice coming from behind to seal a tie at Southend.
They became the first side to beat the Bantams in a cup match this season in the replay, which followed the 1-1 draw in which City fielded ineligible player Curtis Good and initially saw them booted out of the competition.
Brentford boss Uwe Rosler said he was "perplexed" by the FA U-turn which gave his side little time to prepare for the tie.
His worst fears looked like coming true after Kyel Reid, returning after a lengthy lay off with a groin injury, put the Bantams ahead on the half hour when he smashed home a loose ball from 12 yards.
On-loan Fulham striker Marcello Trotta levelled just before the break, firing home from the penalty spot after he was fouled by City defender Carl McHugh.
Former Bee Alan Connell made it 2-1 to the cup specialists in extra time when he converted from the spot after a Shaleum Logan foul on Blair Turgott.
But Trotta pounced again, firing a left-footed drive home into the top corner to equalise.
Substitute Clayton Donaldson made it 3-2 to the hosts by slotting home Harry Forrester's cross, before Forrester sealed it late on with a cool finish in the bottom corner.