Leeds scored three goals in extra time to beat Plymouth Argyle in their FA Cup fourth-round replay.
Brendon Galloway chested the ball in to cancel out Wilfried Gnonto's opener for Leeds and force extra time.
Substitutes Crysencio Summerville and Georginio Rutter scored to ensure Leeds fans did not make the 600-mile round trip to Home Park in vain.
Plymouth's fate was sealed when Ryan Hardie headed in an own goal in the 117th minute.
After a slow start for both Championship sides in wet and blustery conditions, Leeds burst to life when Mateo Joseph waltzed through the Plymouth box before his strike was tipped onto the crossbar by Conor Hazard.
Leeds were denied again by the woodwork moments later when Joel Piroe's powerful effort from the edge of the area rattled off the crossbar.
A momentum shift saw the Pilgrims produce promising attacks of their own, but superb blocks from Sam Byram and Joe Rodon ensured the teams finished an end-to-end first half on level terms.
Piroe and Joseph came close as Leeds dominated the early stages of the second half before Italian forward Gnonto broke the deadlock with a low strike that fizzed through the legs of Ashley Phillips before nestling into the bottom corner of the Plymouth goal.
Plymouth forced their way back into the game when Phillips got on the end of a free-kick into the box and knocked it across the face of goal for Galloway to bundle the ball over the line.
Leeds' Joe Gelhardt and Plymouth's Ryan Hardie came close to clinching victory for their sides in the final minutes of stoppage time, but the woodwork denied the Leeds substitute before Illan Meslier produced a brilliant save at the other end to send the game to extra time.
Summerville came on in the dying moments of the second half and needed little time to make an impact as he cut in on his right foot, sending Phillips the wrong way before placing the ball past Hazard.
The Dutch winger was involved again to set up Leeds' third goal, squaring the ball to Rutter, who slotted the ball into the bottom corner.
Hardie flicked a corner into his own net to end Plymouth's hopes of reaching the fifth round of the FA Cup for the first time since the 2006-07 season.
Leeds boss Daniel Farke told BBC Sport: "Credit to Plymouth, they found a way in the first leg although we were dominant, although we created so many chances, to get a result. It was the same today.
"They always found a way to get a foot in the door and for that we had to dig in and keep going and I loved the attitude today.
"We deserved this. Even if they would go and lead, I was 100% certain that we would win this cup tie because we have done more than enough in 180 minutes in order to deserve it."
Plymouth boss Ian Foster told BBC Sport: "It's quite a sobering scoreline, it doesn't quite reflect the entire game, but they put so much quality and firepower on the pitch late on and we found it quite difficult to deal with it in moments.
"I'm incredibly proud of the players. We've stuck in, we've showed moments of quality ourselves and we're obviously incredibly disappointed to be going out of the competition but I'm really proud of every single player tonight.
"We don't want to make any excuses, but the truth of the matter is we were without eight first-team players tonight. "e can't fill the bench, three 18-year-olds on the pitch for probably 50 minutes of the game so we've done smashing."