Head coach Grant McCann praised striker Tom Eaves after his hat-trick in the 3-2 win at 10-man Rotherham sent Hull through to the FA Cup fourth round.
Eaves ensured a replay was avoided with a stoppage-time header, which completed his treble and settled the tie in dramatic fashion.
The ex-Millers loanee put Hull in front from Dan Batty’s cutback but Rotherham hit back either side of a red card from Adam Thompson for a late challenge on Keane Lewis-Potter.
Michael Smith smashed them level and then a stunning strike from Kyle Vassell sent Rotherham in ahead at the break.
Hull swung the tie in their favour in the second half with Eaves heading them level and then into the fourth round in time added on.
McCann said: “He [Eaves] is getting better and better and finding himself in more dangerous positions and when he is in there he’s a big lump and he can finish. I’m pleased with him.
“My favourite one was the third goal because he anticipated it.
“It was a tough game. I knew it was going to be. I have a lot of admiration for what Paul Warne’s doing.
“We struggled to compete with the first ball and second ball, even with 10 men. We didn’t move the ball with any tempo and just invited them to counter-attack on us.
“We have been to three tough places in QPR, Sheffield Wednesday and Rotherham and won all three. I couldn’t be more pleased.”
McCann brought on internationals Jackson Irvine and Kamil Grosicki as well as danger man Jarrod Bowen after an hour to power them through.
He added: “We were better when we made the changes. It was a bit of a risk but it paid off for us.
“The three boys coming on gave the fans a lift. I didn’t want to use them but had no choice.”
Rotherham manager Paul Warne said: “It seemed a bit harsh. I’m really proud of the team.
“It sounds a bit cheesy when a manager talks about the team after a defeat but I thought we were excellent. I’m really proud to be their manager.
“They’re really disappointed but I will leave the stadium happy. We played 66 minutes without a player and that is asking a lot of the lads.
“I have got good characters. We make them determined and motivated to play for this great club and they give everything.
“My own disappointment was the first 10 minutes – we gave them too much respect. We didn’t start as quickly as I would have liked.
“They brought their superstars on which obviously made a difference. I might have been on the wrong end of a few decisions.
“Unfortunately it wasn’t our day but I am not knocking anything the lads did.”