York boss James Ford heralded the performance of his side after they caused a cup upset at the expense of Swinton.
The City Knights secured their passage into the fifth round with two quick tries, before holding off a late fightback from the struggling Lions.
Ford, whose stock continues to rise following this victory, was full of praise for his team.
“It was a magnificent effort with the attitude being fantastic and yet again they really turned up for each other,” he said.
“They put themselves under a little bit of pressure as Swinton were good with the ball, but we have a desire to work hard for one another and that was enough to take us through.”