Tomori's second-half goal proved to be the winner, but Chelsea endured a scare when substitute Kamil Grosicki scored from a disputed free-kick in the 78th minute via a deflection off Mateo Kovacic.
Victory means Chelsea stay in the hunt to lift the trophy for the second time in three seasons. It also ends a two-game run without a win for Frank Lampard's team.
Chelsea needed an early nerve-settler after intense initial pressure from the hosts. It duly came in the sixth minute when Batshuayi's effort took a deflection after the striker had reacted quickest in the box.
Batshuayi doesn't start regularly, but the Belgium international is prolific in cup competitions:
Buoyed by the early goal, Chelsea turned on the style against a wide-open Hull defence. Mason Mount slid an inch-perfect pass to meet Ross Barkley's well-timed run, but the latter saw his effort saved by George Long.
The pace and intricacy of the move summed up how effectively the Blues were shifting the ball. Callum Hudson-Odoi was switching play from the right with accurate long passes, and left-back Marcos Alonso had plenty of room on the overlap. Kovacic also wasn't wasting his passes at the heart of the engine room.
The Croatian was also combining well with the lively Mount, whose change of pace was making him difficult for Hull to track between the midfield and forward lines. However, the 21-year-old playmaker was guilty of a touch of greed after he opted against teeing up Batshuayi for a tap-in after Kovacic had played him in, instead shooting straight at Long.
Hull's prolific double act Jarrod Bowen and Tom Eaves, who have 20 league goals between them this season, weren't seeing enough of the ball. Eaves did well to get a shot off on the turn three minutes before the break, but the effort lacked power and was easy for Willy Caballero to collect.
Bowen was beginning to get more involved, using skill and running power to go through the Chelsea defence more than once. However, the 23-year-old often chose to shoot rather than playing in a team-mate:
Hull kept the pressure on after the break, with Bowen still at the forefront. A few more impressive breaks from deep nearly yielded an equaliser, but it was the visitors who thought they had killed the game off on 64 minutes, when Barkley lifted a free-kick onto the head of Tomori at the back post.
Barkley and Pedro then combined for the next chance, with the latter chipping just wide after meeting a fine pass from midfield.
The game appeared beyond Hull until Grosicki's free-kick took a significant deflection off Kovacic and beat Caballero, although there was some dispute about the foul after Alonso had challenged Grosicki's fellow sub Josh Magennis.
Grosicki's pace on the flank kept Hull's threat alive in the final minutes. Meanwhile, Magennis was bullying defenders in the air and providing an obvious focal point for the home side.
It wasn't enough, though, with Chelsea doing enough to hold on during tense closing stages.