Steve Bruce's side missed a first-half penalty through Sone Aluko before goals from Curtis Davies, Sunderland old boy David Meyler and Matty Fryatt in the space of nine second-half minutes booked the Tigers' trip to Wembley next month when they will face League One club Sheffield United.
Sunderland failed to make it two Wembley appearances this season after last weekend's beaten Capital One Cup finalists struggled to offer a threat against their former manager's current club.
The Tigers, who had already beaten Sunderland twice in the Premier League this season, wasted a first-half chance when Aluko's poor penalty was easily saved by Oscar Ustari.
A lacklustre quarter-final tie finally sprung into life midway through the second half when Davies rose well to head Tom Huddlestone's clipped free-kick beyond Ustari.
Former Sunderland midfielder Meyler made it 2-0 on 72 minutes when he beat Lee Cattermole to a clearance from a Black Cats corner before racing in on goal to finish past Ustari.
Cattermole then gifted Hull a third goal on 77 minutes when his woeful back-pass was seized upon by Fryatt to rubberstamp his side's place in the last four.
Sunderland boss Gus Poyet will at least now be able to focus on his side's battle to stay in the top flight after the distraction of their knockout heroics, which saw them lose 3-1 to Manchester City in the Capital One Cup final at Wembley last week.
The Uruguayan made six changes to his final line-up, including a rare start for Argentinian striker Ignacio Scocco.
Bruce's men, keen to atone for their 4-1 humbling by Newcastle last week in a game totally overshadowed by Alan Pardew's touchline antics when the Magpies boss appeared to headbutt Meyler, started well and hit the top of the woodwork with a cross-shot from Maynor Figueroa after just four minutes.
Cattermole's dismal day began on a downer when he became embroiled in a furious spat with former team-mate Ahmed Elmohamady after the Egyptian fell heavily under his 12th-minute challenge.
Referee Craig Pawson took no action on that occasion, although Cattermole - sent off in the equivalent league fixture in November which Sunderland finished with just nine men - was booked on the half-hour for an innocuous-looking challenge on Meyler.
The visitors' chances were few and far between, Scocco spooning a Phil Bardsley cross over the bar in the 19th minute as Hull - weakened by the absence of cup-tied pair Nikica Jelavic and Shane Long - dominated despite a distinct lack of cutting edge.
Sebastian Larsson's foul on Aluko gave the Tigers the chance to go ahead from the spot on 34 minutes but Ustari guessed correctly and dived low to his right to gather Aluko's dismal spot-kick.
Ustari got down to stop another Aluko chance towards the end of the first period and the start of the second half was even worse, with neither side apparently willing to make good on their desire to avoid a replay at any cost.
But then came the visitors' late collapse, starting with John O'Shea's foul on Fryatt on the right flank which presented the set-piece from which Huddlestone's inch-perfect delivery found the head of Davies.
Substitute George Boyd's long ball then deceived Cattermole and gave Meyler a clear run on goal four minutes later, the former Sunderland man providing a sweet left-foot finish before bringing out his joke celebration when headbutting the corner flag.
And Sunderland's misery was complete on 77 minutes when Cattermole's blunder allowed Fryatt to pick his spot past Ustari, and seal the Tigers' trip to Wembley.