The Blues were a dominant side throughout the opening half of the game but they managed only goal through Michy Batshuayi in the sixth minute of the Cup tie.
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.
With top goalscorer Tammy Abraham out injured, Michy Batshuayi was given a rare chance to impress, and the Belgium global gave Frank Lampard a timely reminder of his goalscoring abilities, his deflected strike firing Chelsea ahead after just six minutes.
"I think the impetus to bring in a striker or players potentially that can get on the end of these chances we're creating is there, and we have to be really honest about that", he said.
The much changed side of Lampard had started sloppy against a side of Hull supported by a full KCOM stadium, where Kovacic's diagonal pass found Cesar Azpilicueta wide to the right.
It was a punch in the stomach that made Hull stagger.
They were never going to stop and we knew that.
Long ran out of his line to deny Ross Barkley before the English worldwide trailed away, Hull's goalkeeper making another late save when Mount attempted to dink the ball over him.
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"But these games are hard, sometimes you scrape through, sometimes you don't go through when you deserve to".
Bowen came closest to the Tigers, highlighting the quality that led to many admiring looks. He rushed forward and forced the Chelsea defense back before scoring a goal just over Caballero's goal.
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.
Chelsea ended the game just under a third in the last 20 minutes when Pedro shot with a left foot and the Spaniard narrowed again after an attempt by Batshuayi and Tomori.
The Blues are set to get their FA Cup campaign back underway tomorrow evening.
- Hull have actually won none of their 11 FA Cup video games versus Chelsea (D3 L8).
The Blues rode their luck defensively at times after Hull's goal and Grosicki missed a great chance to equalise.
Kamil Grosicki scored late on for Hull and although they pushed hard for the equaliser, Chelsea held on.