Stoke boss Mark Hughes admitted his side "rode our luck" to reach the FA Cup fourth round after they were forced to cling on for a 2-1 win at League One Doncaster.
Jonathan Walters' stunning second-half effort proved enough for the Potters after Rovers striker Nathan Tyson had cancelled out Peter Crouch's early effort for the visitors.
But in a dramatic finish Andy Butler clattered a header against the Stoke bar then Tyson and captain Paul Keegan both had chances to equalise in injury time.
Hughes said: "We rode our luck with a few chances Doncaster had and on another day they could have fallen more kindly for them and might still have been in the hat.
"But we will take any fortune that comes our way. You always understand when you're the away side the home side will have a go to get back in the game and it was a good cup tie.
"I thought Doncaster caused us problems and it has taken two good quality goals from us to take the tie away from them."
Hughes said his decision to make nine changes was out of necessity due to his side's busy schedule but he denied his reshuffle disrespected the competition.
Hughes added: "This was the only opportunity between now and mid-March where we could rest some key players but I still had nine full internationals out there which showed our strength in depth."
Rovers boss Darren Ferguson bemoaned his side's missed opportunities and a second-half penalty appeal after Craig Alcock tumbled in the box.
Ferguson said: "It was a proper Cup tie that went to the wire and we had two great chances at the end but you have got to take them.
"It's really frustrating to think we did so well but we lost. I'm not disappointed with the performance at all, but I am with the result."
Referring to Joselu's challenge on Alcock, Ferguson added: "The key decisions did not go our way.
"The centre-half has grabbed our striker by the throat. It might be seen as sour grapes but it's not because I am just looking at the performance of our players."