Liverpool, who lost the away leg at Bramall Lane 2-1, took a ninth-minute lead through Senegal forward El Hadji Diouf but needed Owen's 107th-minute strike to line up a final with either holders Blackburn Rovers or Manchester United.
Rovers host United on Wednesday with their semi-final tied at 1-1 after the first leg as they bid to reach the final in Cardiff's Millennium Stadium on March 2.
Liverpool, who have won the League Cup a record six times, fully deserved their trip to Wales after keeping a courageous Sheffield United side under control for most of the game.
England midfielder Steven Gerrard, whose side had been under fire after an 11-match winless streak before Saturday's victory at Southampton, told Sky Sports: "We've had a lot stick but it was up to us to prove them wrong.
"It was very tough. Sheffield United were a great team over both legs, you've got to give credit where it's deserved."
But he made it clear that Liverpool were determined to get to Cardiff and to lift the trophy.
"That's what we've come into it for," he said. "The manager's proved he wants to win it from the start by putting strong teams out. Now we've got one game to go."
Owen, whose finishing had been below-par before his goal, said: "I had a couple of chances and the last one was probably the easiest of the lot, so it was nice to score in the end.
"To get in a final is no mean achievement. The first final of the year and we're in it, so we've got to be happy."
Though United's hopes of the club's first major cup final since 1936 were dashed by their first defeat in 16 matches, Neil Warnock's men could have few complaints about the outcome.
Outgunned in midfield and denied any real space in the final third by Liverpool's well-drilled defence during the first half, they showed more fight in the second and extra time -- albeit without creating any clear chances.
Trailing after the first leg, Liverpool's prayer for an early goal was soon answered --
NO MISTAKE
The Senegalese striker made no mistake though when Owen's close range effort was parried, Emile Heskey knocked the loose ball into Diouf's path and his low 20-metre shot gave keeper Paddy Kenny no chance.
Buoyed by only the fifth strike of his first season on Merseyside, Diouf followed up by hitting the crossbar with a miss-hit volley as Liverpool turned the screw.
With their ground attacks broken up by Liverpool skipper Sami Hyypia and fellow defender Jamie Carragher, United's main threat was in the air, with striker Wayne Allison nodding over the bar and defender Phil Jagielka sending a powerful header just wide from a corner before the break.
United enjoyed their best spell midway through the second half with midfielder Michael Brown's free kick tipped over the bar by Kirkland and followed up by two goalmouth melees.
Liverpool soaked up the pressure and then hit back, squandering a string of opportunities.
Owen missed a chance on the break, Czech midfielder Vladimir Smicer volleyed wide, Gerrard had a shot deflected over the bar and fellow England midfielder Danny Murphy headed wide as Gerard Houllier's men converged on the United goal.
Diouf then ballooned a volley before Liverpool's worst nightmare nearly came true.
Kirkland was booked for holding the ball just outside the area after a challenge from Allison and substitute Tommy Mooney smacked in a potent free kick that was deflected away.
Liverpool restored their grip on the game in extra-time and when Owen raced away on the break to tuck home Gerrard's through ball, the outcome was never in doubt.
Despite the modest opposition, Liverpool will want to see Tuesday's victory as a further sign that a frustrating season is finally getting back on track -- three days after they registered their first league win in 12 games at Southampton.