The Blue Square Premier side made a decent fist of things, particularly in the first half of the third round clash when they asked one or two questions of their Premier League hosts.
But in the end, it was a comfortable win for Steve Bruce's side, with the Sunderland boss taking the opportunity to blood some of his youngsters towards the end of the encounter.
Barrow started the game full of purpose and endeavour and tried their luck on five minutes but Marc Goodfellow's strike was comfortably saved by Marton Fulop.
A minute later Sunderland went close but Steed Malbranque fired wide of the target.
Barrow's Phil Bolland then forced a save out of Fulop as the Cumbrians continued to look busy without really getting at a Sunderland backline, which featured skipper and central midfielder Lorik Cana at centre-back.
And any slim hopes the visitors had of pulling off a cup giant-killing more or less went out on the window on 16 minutes.
Steed Malbranque, who had only just returned to the field having had to leave to replace his contact lenses, popped up to put his side in front.
Daryl Murphy played in George McCartney, who pulled the ball back and Fraizer Campbell flicked the ball back off the near post. Malbranque nipped in to fire past Tim Deasy in the Barrow goal.
The Cumbrian outfit refused to be bowed and Goodfellow tried his luck again on 25 minutes but once again Fulop dealt with the effort comfortably.
And the Hungarian shot-stopper was equally as comfortable with Andy Bond on the half hour.
Sunderland were still in first gear but Darren Bent did fire straight at Deasy on 34 minutes.
Jordan Henderson and David Meyler both fired wide before the break and in truth neither keeper was overly worked during the opening 45 minutes.
The hosts improved after the break, although Barrow tested Fulop again on 49 minutes through Jason Walker.
A minute later Campbell should have done better when he headed wide of the target.
Seconds later, the Sunderland striker made amends. Gareth Jelleyman was penalised for handball and Murphy whipped in the resulting free-kick. Campbell got ahead of his marker to direct a diving header past Deasy to make it 2-0.
If Barrow now faced an uphill struggle, they had a mountain to climb just before the hour mark.
Phil Bardsley crossed with his left and Campbell was there again to head home for 3-0.
Barrow were more or less down and out but kept on plugging away in search of a consolation goal.
But it was the Wearsiders doing the majority of the attacking with Bent and his replacement teenager Ryan Noble both forcing saves out of Deasy.
Any more goals would have of course been harsh on Barrow, who battled valiantly throughout but came away with their FA Cup dream shattered
Before the end the visiting support of 7,200 were informed that one of their major routes home had been closed due to bad weather.
Talk about adding insult to injury.