Just four days before facing Barcelona in the first leg of their Champions League last 16 tie, Conte named a much-changed side with Thibaut Courtois, Cesar Azpilicueta, NGolo Kante and Eden Hazard not even included in the Italians squad.
But they still had too much quality for the Championship strugglers as two great strikes from Willian added to goals from Pedro Rodriguez and Olivier Giroud's first for Chelsea put the hosts 4-0 up by half-time.
Once again the Chelsea support showed their backing for the former Juventus boss, but more challenging tests lie ahead in their bid for Champions League glory, and a place back in the competition next year via the top four of the Premier League should they fall short.
Barcelona's visit to the Bridge on Tuesday is followed by consecutive trips to Manchester United and Manchester City on league duty before the return leg at the Camp Nou on March 14.
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"But in the next two weeks we have to play massive games and we must be strong - Barcelona, United and City. We are ready."
Willian did no harm to his case to start against the Catalans with a stunning all-round display capped by his two goals.
"For sure, his performance was impressive," added Conte.
"I hope to see always this type of performance because, when Willy plays in this way, it is a great joy for me, the team, the club and our fans."
- Relieved Giroud -
A former Barca duo combined for the second as Cesc Fabregass lofted pass freed Pedro in behind the Hull defence to slot past David Marshall.
Willian showed he is capable of scoring from range off either foot as his low drive cushioned the post on its way past Marhsall moments later for his 10th goal of the season.
Giroud then cut a relieved figure when he tucked home debutant Emerson Palmieris low cross to round off a first 45 minutes to forget for the visitors.
Hull had the chance to salvage some pride early in the second-half when Fabregas tripped Liverpool loanee Harry Wilson inside the area.
But a dire night for Nigel Adkins men was complete when Willy Caballero saved David Meylers penalty.
And Willian was inches away from the hat-trick his display deserved when another long-range effort came back off the post two minutes from time.
Leicester joined Chelsea in the last eight as Riyad Mahrez provided the spark for the Foxes on his return to the starting line-up.
However, he showed why the runaway Premier League leaders were interested with the teasing cross for Jamie Vardy to head home the only goal in a 1-0 win over Sheffield United.