Match ends, Rotherham United 2, Hull City 3.
Hull City striker Tom Eaves scored a last-minute winner to complete a hat-trick and knock 10-man Rotherham United out of the FA Cup in the third round.
It was cruel on the Millers, who battled hard after losing defender Adam Thompson to a first-half red card.
The League One side led 2-1 at the break thanks to goals from Michael Smith and Kyle Vassell, after Eaves had put their Championship opponents ahead.
They fought valiantly, but Eaves struck twice more to send Hull through.
- Live: FA Cup third-round - in-play clips, radio and text coverage
- Watch all the latest FA Cup goals, highlights and reaction here
- Where will the shocks be? Ladhood star Liam Williams takes on Lawro
- How to follow the FA Cup third round on the BBC
A replay would have been just reward for the endeavour shown by Paul Warne's League One side, who were looking to book a place in the fourth round for the first time since 2002, following Thompson's early sending-off for a lunging challenge on Tigers teenager Keane Lewis-Potter.
It would also have meant Vassell's stunning goal was not in vain.
After Eaves turned home a Dan Batty pull-back from close range, Smith's powerful 12-yard strike into the top corner looked like being the goal of the game.
But his striker partner Vassell had other ideas, allowing a throw-in on the left to bounce over his shoulder before he volleyed past the diving Matt Ingram from the corner of the penalty area.
In the second period, Rotherham looked secure in their lead despite their man disadvantage against a higher-division opponent.
But Hull boss Grant McCann, who made eight changes from the Tigers' previous match, turned the match in his team's favour by sending on top-scorer Jarrod Bowen, Kamil Grosicki and Sean Irvine.
Just a few minutes later Grosicki crossed from the left for Eaves to head in and with time running out, he nodded home again to finally end Rotherham's resistance.
Hull boss Grant McCann told BBC Radio Humberside:
(On sending-off) "I know Adam Thompson, I've played with him for Northern Ireland. That's not like him to tackle like that, it was horrible.
"If Keano's leg had been still, he could have broken his leg. He's an honest pro, a good boy, Adam, maybe he just mistimed it but it didn't look good from where I was.
(On Eaves hat-trick) "He's getting in more dangerous areas. As a centre-forward you don't just have to make one run, you have to make four, five, maybe six or seven and that's slowly but surely sinking in.
"I talk to him all the time about how you might need 15, 16 runs in a game, you might only get it once or twice and you've got to take your chance."
Rotherham manager Paul Warne told BBC Radio Sheffield:
"I'm really proud of the team. We had 66 minutes without a player, which asked a lot of the lads out of possession.
"They made subs, bringing their superstars on, which obviously made a difference, but I still thought we defended well.
"I've good characters (in the team). We get them fit, we make them determined and motivated to play for this great club and they give everything.
"I'm happy with what I've seen. Sometimes you get the rub of the green, sometimes you don't and I don't think our play today got the rub we deserved."
- 5ThompsonBooked at 24mins
- 20IhiekweBooked at 72mins
- 19OgbeneSubstituted forLadapoat 78'minutes
- 24SmithSubstituted forMorrisat 90+1'minutes
- 7VassellSubstituted forLindsayat 71'minutes
- 21FlemingSubstituted forBowenat 61'minutes
- 8BattySubstituted forIrvineat 61'minutes
- 37Da Silva LopesBooked at 86mins
- 19BowlerSubstituted forGrosickiat 61'minutes
- 9EavesBooked at 90mins
- Anthony Backhouse
- Shots on Target
Second Half ends, Rotherham United 2, Hull City 3.
Corner, Hull City. Conceded by Matthew Olosunde.
Jamie Lindsay (Rotherham United) hits the right post with a header from the centre of the box.
Tom Eaves (Hull City) is shown the yellow card for excessive celebration.
Goal! Rotherham United 2, Hull City 3. Tom Eaves (Hull City) header from the left side of the six yard box to the top right corner. Assisted by Ryan Tafazolli following a corner.
Corner, Hull City. Conceded by Michael Ihiekwe.
Substitution, Rotherham United. Carlton Morris replaces Michael Smith.
Foul by Matthew Olosunde (Rotherham United).
Josh Bowler (Hull City) wins a free kick in the defensive half.
Foul by Matthew Olosunde (Rotherham United).
Keane Lewis-Potter (Hull City) wins a free kick in the defensive half.
Attempt blocked. Herbie Kane (Hull City) right footed shot from outside the box is blocked.
Corner, Hull City. Conceded by Matt Crooks.
Freddie Ladapo (Rotherham United) wins a free kick in the defensive half.
Leonardo Da Silva Lopes (Hull City) is shown the yellow card for a bad foul.
Foul by Leonardo Da Silva Lopes (Hull City).
Attempt saved. Kamil Grosicki (Hull City) left footed shot from a difficult angle on the left is saved in the centre of the goal.
Corner, Hull City. Conceded by Daniel Iversen.
Foul by Freddie Ladapo (Rotherham United).