After a scrappy and goalless first half, the visitors twice came back from a goal down against a youthful United side before "Little Pea" Hernandez skipped past defenders to settle the tie in the 90th minute.
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"When he came on, you just know that if he gets a chance he is going to take it," United manager Sir Alex Ferguson, who replaced his entire starting line-up from the weekend, told Sky Sports television.
Premier League West Bromwich Albion roared through to the last eight with a thumping 4-1 victory at former England manager Sven-Goran Eriksson's Championship side Leicester City.
Wigan Athletic beat second division Swansea City 2-0 with Argentine striker Mauro Boselli scoring his first goal for the club since his signing from Estudiantes.
The run of fourth division Northampton Town, who knocked out Liverpool at Anfield on penalties, ended at second division Ipswich Town where they lost 3-1 despite opening the scoring with a looping Liam Davis shot.
PENALTY AGONY
Third division Brentford, who knocked out Everton on penalties in the previous round, took their second Premier League opponents to spot-kicks before losing 4-3 at Birmingham City.
The hosts, rocked by a 68th-minute Sam Wood volley, had escaped by the skin of their teeth thanks to a Kevin Phillips equaliser deep into stoppage-time.
United, with a team Ferguson described as a glimpse into the future, were lacklustre in the first half before coming alive.
"It was a very open game in the second half, both teams played very well," said Ferguson.
The Scot praised Hernandez, who scored twice at Stoke City as a stand-in for the injured Wayne Rooney on Sunday, for his attitude and commitment.
"We tend to build up heroes very quickly here but the boy's justifying the praise at the moment," he said of the 22-year-old striker who had come on only nine minutes before his goal.
"He's such a great professional, the kid. He's first in and last out of the training ground every day and his goalscoring is quite rightly getting him a lot of credit and praise now."
Portuguese striker Bebe, making his first start for United, had opened the scoring with a strike deflected in by George Elokobi who then equalised with a header.
Park Ji-sung made it 2-1 in the 70th but Wolves, who had not scored at Old Trafford since 1980, refused to lie down and Kevin Foley again levelled with a low shot in the 76th.
United also brought on 17-year-old Ravel Morrison, tipped as a big talent for the future, as a substitute in the dying seconds.
