The Black and Whites, five times winners of the competition, ran in 11 tries to end a brief cup run which had previously taken their part-time opponents past amateurs Hunslet Club Parkside and League One North outfit Wales Crusaders.
The ever evasive and inventive Connor crossed twice, Wynne went in for his treble while Adam Swift, Andre Savelio, Josh Griffin, Carlos Tuimavave, Mitieli Vulikijapani and Jordan Lane all scored for Hull.
Sheffield, most famous for their shock cup final victory over Wigan in 1998, managed to breach the Black and Whites' line twice through Kris Welham and Tom Holmes.
Despite the margin of victory, Hodgson was full of praise for Aston’s team, saying: “I thought we respected Sheffield very well, I’m really pleased. I think we saw another level of growth from what we’re trying to achieve here.”
The tie, played at Featherstone's Millennium Stadium due to the Eagles' new Olympic Legacy Park Stadium not being completed until late May, pitched against each other coaches Mark Aston and Brett Hodgson who had both, during their playing days, won the Lance Todd Trophy man of the match award in winning Challenge Cup final teams.
The Eagles had won their last four league and cup games but Super League side Hull offered a significant step up in size and class.
Hodgson's Hull, armed with their strongest available side and bolstered by a first appearance of the season for Samoa international Tuimavave, back after a hamstring injury, took less than two minutes to open the scoring through full-back Connor.
Connor scooted over from close range and Ben McNamara converted with the first of seven goals.
Sheffield, playing up Featherstone's slope, tried to respond with winger Matty Chrimes, scorer of seven tries in his last three games, threatening down the left flank.
But seconds later his Hull counterpart Swift raced clear from his own half and ran 70 metres to help double the Black and Whites' advantage.
Vila Halafihi was held up as the Eagles, helped forward by penalties and a knock-on, pressed again for a response and only a superb last-gasp tackle by Wynne prevented Chrimes crossing in the corner.
A mazy run by Connor came to nothing when his final pass went astray. But Tuimavave put Wynne over and Savelio then scored following a wonderful Connor 40-20.
Savelio then created a second try for Wynne to help give FC, whose supporters far outnumbered those of nomadic Sheffield, a 26-point half-time lead
Connor put Griffin over to set the scoreboard moving again after the break, with further tries from Tuimavave, Connor, Vulikijapani, Wynne and Lane ensuring Hull's place in the last eight.
Welham, once with FC's city rivals Hull KR, and Holmes claimed consolation tries for the Eagles either side of the hour, both converted by 36-year-old half-back Anthony Thackeray, who began his long career at Hull.
The game finished worryingly with Sheffield prop Brandon Douglas being stretchered off after mistiming a tackle eight minutes from time.