On-the-whistle report: Rotherham United 2 Hull City 3

The Millers had right-back Adam Thompson sent off midway through the first half but they were still right in the contest deep in added time when the Championship Tigers edged the third-round tie.

Tom Eaves' hat-trick header after a corner did the late damage but there had been a missed offside in the build-up which put the seal on a woeful display by the officials.

Paul Warne's League One side lost Thompson because of a late challenge in the 24th minute when the score was 1-1 yet they swept back into the lead before the break and held their advantage in a pulsating clash until past the hour mark.

Rotherham, playing against opponents from the division above, scored two superb goals despite playing for so long with a man down and will feel they were worthy of draw.

They fell behind in the 16th minutes when Dan Batty crossed low from the right and former Millers loan striker Tom Eaves swept the ball home.

But they were behind for only five minutes before Michael Smith restored parity with a thumping finish.

The centre-forward received the ball from Chiedozie Ogbene with his back to goal then turned and fired a fierce shot well beyond Tigers goalkeeper Matt Ingram.

The Millers were more than matching their second-tier opponents but suffered a huge setback within minutes of the equaliser whem Thompson received a straight red card for a late challenge on Keane Lewis-Potter.

However, the home side switched to a 4-4-1 formation, refused to let up and took the lead two minutes before the break with a wonder-goal.

Kyle Vassell let a Matt Olosunde throw-in on the left run across his body and flashed a stunning 20-yard volley from an angle into the far top corner of the net.

Despite their numerical disadvantage, Rotherham remained a threat after the break but the introduction of Jarrod Bowen, Kamil Grosicki and Jackson Irvine in the 61st minute turned the contest in the Tigers' favour.

Dan Iversen had to save in quick succession from Bowen and Eaves but was powerless to prevent Eaves heading a 66th-minute leveller.

Still the Millers refused to yield and Matt Olosunde shot wide at the back post ten miutes later as he stretched to control Ogbene's cross.

Iversen kept the scores level in the 84th minute, spreading himself to thwart Grosicki with his leg, before the drama at the end.

Brave Rotherham almost came again and visiting skipper Reece Burke diverted the ball on to the frame of his own goal before referee Anthony Backhouse blew for time and was booed off.

Rotherham (4-4-2): Dan Iversen; Adam Thompson, Michael Ihiekwe, Richard Wood, Matt Olosunde; Chiedozie Ogbene (Freddie Ladapo 79), Dan Barlaser, Matt Crooks, Ben Wiles; Kyle Vassell (Jamie Lindsay 70), Michael Smith (Carlton Morris 90+1). Subs not used: Lewis Price, Trevor Clarke, Julien Lamy, Jake Hastie.

Hull City (4-3-3): Matt Ingram; Robbie McKenzie, Reece Burke, Ryan Tafazolli, Brandon Fleming (Jarrod Bowen 61); Leonardo Da Silva Lopes, Dan Batty (Jackson Irvine 61), Herbie Kane; Josh Bowler (Kamil Grosicki 61), Tom Eaves, Keane Lewis-Potter. Subs not used: George Long, Eric Lichaj, Sean McLoughlin, George Honeyman.

Goals: Smith 21, Vassell 43 (Rotherham); Eaves 16, 66, 90+2 (Hull).

Red card: Thompson 24 (Rotherham).

Referee: Anthony Backhouse (Cumbria).

Attendance: 6,044 (1,803).