The League One side came from behind to beat Championship side Batley Bulldogs 16-12 in their fifth round tie at the Keepmoat Stadium.
They are the lowest ranked side left in the competition.
“We are pretty busted at the moment and we had a lot of players playing out of position but the boys turned up for each other on the day and worked hard and sometimes that is all you have to do to give yourselves an opportunity to win games and we took it,” said head coach Richard Horne.
Long-serving Kyle Kesik took the man-of-the-match award standing in for injured play-maker Jordan Howden in the unaccustomed role of stand-off.
Doncaster Rovers defender ruled out for one month
Doncaster Rovers: Former recruitment boss joins Watford in similar role
The difference of opinion and slice of luck that led Jack Degruchy to Doncaster Rovers
Doncaster Rovers player ratings from the dramatic draw at AFC Wimbledon
Why Doncaster Rovers feel the best is yet to come despite a ‘solid start’
“I only decided to play him there at the last minute,” said Horne.
“I did have it in my head to play (dual-registered) Charlie Patterson-Lund there because he’d played stand-off at junior level.
“But for him to come into a team not really knowing anybody would have been hard and playing Kezzie there obviously worked.
“He’d gone well there in a team run and that helped persuade me to play him there.”
Horne was also impressed by the contribution of veteran Papua New Guinea centre Menzie Yere in his first game for the club.
“Menzie was able to give us some useful background information on Batley, who we haven’t played in a competitive game for a few years,” said Horne.
“He also has a lot of experience and scored an important try and I thought he played really well.
“He’s not played for Sheffield this season and he’s come here to get game time and we’ll see where it goes from there.”
Reflecting on the game Horne said: “Their line speed was good and their defence aggressive early on and we couldn’t get out of our own half.
“But we hung in there, defended well and didn’t panic and after going close a couple of times we came in leading 6-0.”
Despite Batley scoring twice in the third quarter to lead 12-6 Horne remained positive.
“I knew that we would get further chances; we just had to be clinical when they occurred and we were.
“It was a bit nerve-racking at the end when they were throwing the ball all over the place but we held out to get the job done and we’ll see now who we get in the sixth round draw on Monday night."