From there the Eagles took full control of the encounter with tries from Gavin Brown and Johnny Woodcock giving them a 16-4 interval lead.
Worrincy added his second after the restart with touch downs from Jimmy Walker and Andy Hay completing the rout, with a Swinton score from Dave Alstead.
Sheffield chief executive Mark Aston, who played when the Eagles lost out to Keighley cougars at this stage three years ago, said that the result was a fantastic reward for everyone at the club.
Aston said: "For the last seven years we have worked very hard to keep the club alive.”
Today is a reward for everyone involved at the club, for the fans, for the sponsors, the staff, the players, the board of directors and everyone who has put so much into keeping Rugby League alive in the city.”
Aston added that it was important Sheffield work hard to try and consolidate their position in NL1.
"We now have to consolidate our achievement and must not sit back on our laurels and make sure that this time next year we are still in a position to be playing National League One rugby."