Elsewhere, holders Chelsea progressed with a 3-1 home win over League One Huddersfield Town, with Frank Lampard scoring twice, while League Two Bristol Rovers upset League One Southampton 1-0 with a late goal by Rickie Lambert on his 26th birthday.
In two all-Championship ties, West Bromwich Albion thrashed Coventry City 5-0 away and Cardiff City beat Wolverhampton Wanderers 2-0.
Brian Howard's 25-yard strike, moments after the Yorkshire club had a penalty appeal turned down, sealed a memorable victory for the Championship side and added to the pressure on under-fire Reds boss Rafael Benitez, who made a number of changes to his side.
Liverpool, the five-time European champions, broke the deadlock in the 32nd minute when striker Dirk Kuyt poked in a cross from fellow Dutchman, Ryan Babel.
But Barnsley were level before the hour mark when Stephen Foster headed in a cross from Martin Devaney.
Harry Kewell almost wrapped up the tie for Liverpool when his shot hit the crossbar as the Reds surged on.
Meanwhile, keeper Luke Steele, on loan from West Brom, had a Barnsley debut to remember with several fine saves before Howard struck in an FA Cup victory to remember.
|Nani helped Man Utd brush Arsenal aside [AFP]|
Benitez, despite seeing his side twice fall behind to non-league Havant and Waterlooville in the fourth round at Anfield, opted to leave inspirational captain Steven Gerrard on the bench while first-choice goalkeeper Pepe Reina and star striker Fernando Torres didn't feature at all in the matchday squad.
Liverpool's Spanish boss was clearly trying to protect his stars ahead of Tuesday's Champions League clash against Inter Milan in the only competition the Merseysiders now have a realistic chance of winning this season.
The eagerly-awaited clash between Arsenal and Manchester United - England's two top teams - turned out to be a one-sided affair as Manchester United thumped 10-man Arsenal 4-0 at Old Trafford.
United were 3-0 up after 38 minutes through Wayne Rooney, Darren Fletcher and Nani as Arsenal's injury-hit side looked badly off the pace and short of motivation.
United, also without some leading players, were just as dominant after the break and Arsenal suffered a further setback five minutes after the restart when Emmanuel Eboue was sent off for a wild challenge on Patrice Evra.
Both teams then made substitutions to rest players for midweek Champions League games but United remained on top and got their fourth goal with another Fletcher header after 74 minutes.
Frank Lampard scored his 100th goal for Chelsea, with a low shot from 18 yards in the 18th minute.
But Huddersfield, who knocked out Premier League Birmingham in the third round, shocked the crowd just moments before half-time when Michael Collins struck from 12 yards to equalise after a pass from James Berrett.
|Lampard has now scored 101 goals |
for Chelsea [Reuters]
Lampard then settled Chelsea's nerves in the 60th minute when, after his shot was blocked by Huddersfield keeper Matt Glenon, he followed up to score from the rebound.
The result was put beyond doubt when Salomon Kalou's shot went in off Glennon 20 minutes from time.
Rickie Lambert's deflected free-kick six minutes from time sealed Bristol Rovers's second notable success of this season's FA Cup after the team sitting 13th in English football's third tier had knocked out Premier League Fulham on penalties in the third round.
West Brom went ahead against Midlands rivals Coventry through Chris Brunt's 12th minute header. Things got worse for the Sky Blues when Michael Doyle was unluckily sent-off for a challenge on Zoltan Gera.
Then a mistake from Coventry goalkeeper Andy Marshall allowed Roman Bednar to double the Baggies' lead in the 59th minute before the Czech, on loan from Hearts, made it 3-0 from the penalty spot.
Two goals in as many minutes from Ishmael Miller and Gera compounded managerless Coventry's woes.
Cardiff, the only non-English club to win the FA Cup, needed just two minutes to take the lead at Ninian Park when Peter Whittingham fired home after being played in by Jimmy Floyd Hasselbaink.
The much-travelled former Chelsea striker then doubled the Welsh side's lead nine minutes later after Whittingham turned provider.
Premier League Portsmouth, a contender to break the 13-year monopoly of the Cup enjoyed by the 'Big Four' of Arsenal, Manchester United, Chelsea and Liverpool, are away to struggling Championship side Preston on Sunday.
Also in action Sunday are top-flight Middlesbrough, away to Sheffield United, which will be Kevin Blackwell's first match in charge of the mid-table Championship club after he replaced Bryan Robson this week.