An early opener from striker Batshuayi calmed any Chelsea nerves, before Tomori's header stretched their lead in the second half. 

Hull's reply was a fortunate one, Kamil Grosicki's free-kick taking a giant deflection off Mateo Kovacic.

The host began to believe they could force a replay, but Chelsea withstood the late scare to clinch a place in the last 16 of the competition.

Chelsea swept ahead in the sixth minute from their first serious attack, with the ball falling to Batshuayi close to the penalty spot. The Belgian striker clattered his shot and a deflection off Ryan Tafazolli carried it beyond George Long in the Hull goal.

That made it look bleak for the hosts, given they had never beaten Chelsea in 10 previous FA Cup matches.

Despite showing eight changes from the side that drew with Arsenal on Tuesday, Chelsea's starting XI was strong and signalled boss Frank Lampard's eagerness to win the tie at the first attempt.

Lampard, a four-time FA Cup winner in his playing days, would have been encouraged by Chelsea's forward momentum as Cesar Azpilicueta had a shot blocked before Batshuayi saw an effort deflect wide.

The visitors should have doubled their lead when Ross Barkley made a bright run through the heart of the Hull defence, but the England midfielder's strike was unconvincing and Long blocked, with the Hull goalkeeper later also twice denying Mason Mount and parrying an Azpilicueta shot.

Lampard led Derby County to the fifth round last season before Brighton and Hove Albion ended their campaign, but with Chelsea the trophy is always a target.

The FA Cup represents their best chance of silverware this season, given the Premier League is a Liverpool procession, their EFL Cup campaign is over, and Bayern Munich await the Blues in the Champions League's first knockout round.

Jarrod Bowen has been a goalscoring phenomenon in the second tier of English football and gave a glimpse of his quality just before the hour with a darting run from midfield and a shot that cleared the Chelsea bar by barely a foot.

Hull's hopes were fading when Tomori headed a wonderfully clipped Barkley free-kick inside the left post in the 64th minute for Chelsea's second.

Pedro drilled narrowly wide before chipping into the side-netting, before Hull's reply came with 12 minutes remaining when substitute Grosicki's free-kick took its wild deflection off Kovacic and flew inside the left post.