Fraizer Campbell struck his first goals for three months to head Sunderland into the fourth round at the expense of brave non-Leaguers Barrow.
The Blue Square Premier side had Steve Bruce's men on the rack in a storming start which saw Phil Bolland, Paul Bond and Marc Goodfellow all come close.
But Steed Malbranque's 17th-minute opener set the home side on their way in freezing conditions and Campbell's brace early in the second period saw the Premier League sidesafely into the next round.
Campbell, whose only previous goal this season came in the Carling Cup against Birmingham in September, broke the hearts of about 8,000 away fans massed in the South Stand.
Barrow were dreaming of greater things in a stunning start with Goodfellow's first effort blocked by David Meyler in the box in the third minute.
Bond skidded a shot into home goalkeeper Marton Fulop's arms and the visitors came even closer in the ninth minute when captain Bolland hammered a 30-yard free-kick which Fulop tipped wide.
But Sunderland grabbed a barely deserved lead in the 17th minute when Campbell played a deft back-heel into the path of Malbranque, who swept home a low shot from eight yards.
The second arrived in the 52nd minute when Daryl Murphy swung in a free-kick from the left and Campbell directed a header past Deasy into the bottom corner.
The game was over on 58 minutes when Campbell nodded in a cross from the right by Phillip Bardsley.
Man of the match: Fraizer Campbell (Sunderland)
* With agencies
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The Penguin
Starring: Colin Farrell, Cristin Milioti, Rhenzy Feliz
Creator: Lauren LeFranc
Rating: 4/5
The Bio
Hometown: Bogota, Colombia
Favourite place to relax in UAE: the desert around Al Mleiha in Sharjah or the eastern mangroves in Abu Dhabi
The one book everyone should read: 100 Years of Solitude by Gabriel Garcia Marquez. It will make your mind fly
Favourite documentary: Chasing Coral by Jeff Orlowski. It's a good reality check about one of the most valued ecosystems for humanity
MATCH INFO
Uefa Champions League semi-final, second leg
Real Madrid (2) v Bayern Munich (1)
Where: Santiago Bernabeu, Madrid
When: 10.45pm, Tuesday
Watch Live: beIN Sports HD
Our legal columnist
Name: Yousef Al Bahar
Advocate at Al Bahar & Associate Advocates and Legal Consultants, established in 1994
Education: Mr Al Bahar was born in 1979 and graduated in 2008 from the Judicial Institute. He took after his father, who was one of the first Emirati lawyers
Joker: Folie a Deux
Starring: Joaquin Phoenix, Lady Gaga, Brendan Gleeson
Director: Todd Phillips
Rating: 2/5
The specs
Engine: 3.0-litre six-cylinder turbo
Power: 398hp from 5,250rpm
Torque: 580Nm at 1,900-4,800rpm
Transmission: Eight-speed auto
Fuel economy, combined: 6.5L/100km
On sale: December
Price: From Dh330,000 (estimate)
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Pad Man
Dir: R Balki
Starring: Akshay Kumar, Sonam Kapoor, Radhika Apte
Three-and-a-half stars
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The Dictionary of Animal Languages
Heidi Sopinka
Scribe
The specs
Engine: 1.5-litre turbo
Power: 181hp
Torque: 230Nm
Transmission: 6-speed automatic
Starting price: Dh79,000
On sale: Now
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The specs
Engine: Direct injection 4-cylinder 1.4-litre
Power: 150hp
Torque: 250Nm
Price: From Dh139,000
On sale: Now
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