Liverpool led through Dirk Kuyt but a Stephen Foster equaliser and brilliant goalkeeping by debutant Luke Steele kept Barnsley in the game before Howard drove in the winner.
Frank Lampard scored twice as holders Chelsea progressed with a 3-1 home win over League One (third division) Huddersfield Town while League Two Bristol Rovers upset League One Southampton 1-0 with a late goal on his 26th birthday by Rickie Lambert.
In two all-Championship ties, West Bromwich Albion thrashed Coventry City 5-0 away and Cardiff City beat Wolverhampton Wanderers 2-0 while Manchester United faced Arsenal at Old Trafford later on Saturday.
After Saturday's six ties only two Premier League teams will be in Monday's quarter-final draw and the remaining two in the competition, Portsmouth and Middlesbrough, both face tough away games at Preston North End and Sheffield United respectively.
Liverpool will still be wondering how they failed to progress after creating countless chances.
However, having struggled to get past Luton and minor league Havant and Waterlooville in previous rounds, the home fans must have been nervous as they failed to make their superiority count.
They went ahead after 32 minutes when Ryan Babel crossed for Dirk Kuyt and the Dutchman who had not scored since December could not miss.
Barnsley levelled after 57 when Martin Devaney crossed for centre back Foster to score with a firm header.
Yossi Benayoun and Lucas both hit the bar for Liverpool while Steele, the 23-year-old on loan from West Brom, saved superbly to deny Benayoun, Crouch and Harry Kewell.
Liverpool manager Rafa Benitez, who had opted to rest top striker Fernando Torres with an eye on his midweek Champions League game against Inter Milan, did throw on Steven Gerrard as a late substitute but even the England midfielder could not find a way through some desperate defending.
Barnsley looked to have been denied their chance to win it when they were denied a late penalty claim after Howard was brought down, but he kept his concentration and seconds later struck his superb winner from the edge of the box.
"It's fantastic we've come here to enjoy the day, we had a game plan. From the first minute we worked very, very hard and got the rewards," Barnsley manager Simon Davey told Sky Sports News.
"Liverpool were always going to put us under pressure but there were some fantastic last-ditch tackles in the box and we've nicked it at the end.
"It's a fairy tale. To score a last minute winner at the Kop end, that will live with the players all their lives."
Howard, a Liverpool fan as a boy, said he was busy "whingeing at the ref" over his penalty claim when the ball came back to him.
"I was that tired I thought I'd just kick it and if it goes in the stand it'll waste time," he said.
"I'm still away with the fairies at the moment, I might be able to describe the feeling on Monday."