Pedro scored the second when he slipped the ball under David Marshall after latching onto Cesc Fabregas' excellent halfway line pass.
Hull's focus will hereafter be on their attempts to preserve the Championship status and to avoid a second successive relegation, and their manager Nigel Adkins, 52, said: "We'd come with a game-plan and within a couple of minutes it goes out of the window".
At the end of a week that began with his job in doubt, Conte will take two victories, seven goals scored and none conceded. We were not close enough in the first, but the second half was a totally different story. The most important thing is that we are in the next round.
And the former Exeter man, who can also perform as a midfielder, did not look out of place alongside the experienced Gary Cahill and Antonio Rudiger in the FA Cup, marshalling the pair and making some well-timed blocks and interceptions.More news: Buccaneers release Doug Martin, who ran out of chances in Tampa
Chelseas Gary Cahill and Hull City's Jon Toral challenge for the ball (Picture: Adam Davy/PA Wire).
The wonderful Willian nearly completed his hat-trick late on when hitting the post from 30 yards, but Chelsea eased to victory regardless, leaving Championship strugglers Hull to focus on preventing back-to-back relegations.
- Willy Caballero has saved five of the last eight penalties he has faced in all competitions (excluding shootouts). But to finish this game and to keep the clean sheet was very important. After exchanging a neat one-two with Giroud 30 yards out, he drove towards the penalty area and drilled a low shot into the bottom corner from 25 yards. "It's relieved me a little bit", he said.
And his line-up took just two minutes to crumble under pressure as Willian gave Chelsea the lead, before going on to concede another three before half-time.