WATCH - Rotherham United 2 Hull City 3: Late hat-trick winner for Tom Eaves breaks Rotherham's hearts
The Tigers had trailed against the League One high-fliers for a long spell of the third round tie and there would have been no complaints if Rotherham had held on for a replay.
They had seen defender Adam Thompson red-carded for a high, reckless tackle on Keane Lewis-Potter as early as the 23rd minute.
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Hide AdYet Hull had trailed since going behind to Kyle Vassell’s amazing 43rd minute volley as 10-man Rotherham simply refused to yield.
Indeed, the hosts only seemed to get stronger at the start of the second period and, so, it was no surprise when Grant McCann turned to his major weaponary on the bench in the 61st minute.
In fact, the head coach - who had made eight changes to the side that beat Sheffield Wednesday on New Year’s Day - used all three of his substitutions at once with top scorer Jarrod Bowen, fellow striker Jackson Irvine and Kamil Grosicki all brought on to try and bring some much-needed invention.
It worked almost instantly; Bowen and Irvine both had efforts denied by Daniel Iversen in quick succession.
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Hide AdIt only delayed the inevitable, though, as Eaves rose to connect with a delfected cross to head in his second goal to level in the 65th minute.
From there, it was all Hull as the Championship club looked for the winner.
It looked like they would be denied until Eaves, the 27-year-old striker, rose to head in again in the 93rd minute, breaking Rotherham hearts.
Even at the death, Paul Warne’s side saw a late effort hit the post but there was no reprieve.
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Hide AdHull had won three of their four games over the festive period and this was a third successive victory.
They gave a debut to Herbie Kane, the 21-year-old Liverpool midfielder who only joined yesterday on loan for the rest of the season.
Rotherham are riding high in League One, up to second having won their previous three games and being unbeaten in the last five.
Right-back Thompson was handed a straight red card following his challenge on Lewis-Potter, the talented youngster who was making his first start for Hull.
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Hide AdHowever, the set-back did not deter the hosts who - despite being down to 10 men - took the lead just before the break.
On the left corner of the penalty area, Vassell allowed a throw-in to bounce past him before turning to strike a stunning first-time right-footed shot that left Hull keeper Matt Ingram with no chance.
It was a brilliant effort but nothing that Rotherham did not deserve; they had continued in their positive fashion even after Thompson’s dismissal.
It was only Northern Ireland international Vassell’s third goal in 40 games for the Millers since joining from Blackpool 18 months ago but his second in three matches.
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Hide AdRotherham had already shown great spirit to bounce back from going behind in the 16th minute.
They had enjoyed the better of the play, Vassell going close with a left-footed effort that just went over the bar, only to see Hull strike with their first effort.
Dan Batty, the midfielder who was as busy as ever for the Tigers, surged into the box and pulled back for Tom Eaves to simply turn in.
Still, the hosts continued to probe and Ryan Tarazolli was needed to make a timely challenge just as Michael Smith was about to pull the trigger.
There was no denying Smith, though, in the 20th minute.
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Hide AdChiedozie Ogbene rifled in a low cross and the striker was given acres of space to turn and fire in a thunderous shot from 15 yards out.
However, Championship Hull came back to gain their place in the draw.
Rotherham United: Iversen; Thompson, Ihiekwe, Wood, Olosunde; Ogbene (Ladapo 79), Crooks, Barlaser, Wiles; Vassell (Lindsay 72), Smith (Morris 90).
Hull City: Ingram; McKenzie, Burke, Tarazolli, Fleming (Bowen 61); Batty (Irvine 61), Da Silva Lopes, Kane; Bowler (Grosicki 61), Eaves, Lewis-Potter.
Referee: A Backhouse