A well-taken Olivier Giroud goal secured a fourth consecutive Europa League victory and guaranteed our place in the round of 32 as BATE Borisov were beaten in Belarus.
Giroud pounced early in the second half, arriving in the box to meet a superb Emerson Palmieri cross and head home the only goal of the game as we edged a tight contest which was played in bitterly cold conditions.
The home side struck the woodwork in each half, and the Blues went close on a couple of occasions after taking the lead through Ross Barkley and Giroud, whose powerful header was tipped over the bar.
There was further positivity as Eden Hazard, having played 30 minutes at the weekend, completed an hour of the game, while 18-year-old Callum Hudson-Odoi came on for the closing stages.
With regards to team selection, Hazard was restored to the starting line-up and there was also a place in the side for Giroud, who tasked with leading the line having missed the win over Crystal Palace.
In midfield, Ruben Loftus-Cheek, scorer of a hat-trick against BATE at the Bridge, and Barkley started a game together for the first time this season, with Jorginho operating in a slightly deeper role, and there were wholesale changes made to the back four.
A trademark run from Hazard led to our first opportunity as the Belgian, who left a host of BATE defenders in his wake, found Pedro just inside the penalty area. The Spaniard shifted back inside and saw his left-footed curler charged down, before Barkley’s drive from distance was also blocked.
Barkley had started to the right of Jorginho, with Loftus-Cheek on the left, but there were a couple of occasions early in the contest when passes in that area of the pitch went astray.
It was the home side, however, who went close to taking an early lead when Dmitri Baga crashed a strike against the post from 25 yards out in the 11th minute. There appeared to be little danger when the midfielder picked the ball up, but the shot was well hit and with Kepa beaten, only the upright prevented us from falling behind.
Moments later BATE threatened again, with Kepa getting down well to scoop away a header from Stanislav Dragun, who had got on the end of a corner inside the six-yard box, before Giroud’s strike from a tight angle was deflected behind at the other end.
Loftus-Cheek and Barkley swapped positions around the 20-minute mark, but despite the fact we were seeing plenty of the ball, we were yet to seriously test Denis Scherbitski in the BATE goal as the game approached the half-hour stage.
The driving runs of Hazard and Loftus-Cheek, who had both shown glimpses of their abilities to go past opponents, had been our biggest source of positivity, but the home side were getting large numbers behind the ball when we were in possession and making themselves far more difficult to break down than they had been at Stamford Bridge.
Five minutes before half-time we almost profited from a slick passing move which had involved Pedro and Jorginho, with Loftus-Cheek thwarted just as he went to pull the trigger, and from the resulting corner Giroud flicked a header just wide.
The team emerged for the second half unchanged and undoubtedly looking to offer more of a threat from an attacking perspective than we had in the opening 45 minutes, and it didn't take long as just seven minutes after the restart we took the lead.
The goal owed much to the creativity of Emerson, who provided a delightful cross from out on the left-hand side which was met emphatically by Giroud, who powered his header beyond Scherbitski at his near post.
It was the Frenchman's first goal of the season, and one which had given us a crucial advantage in the contest.
BATE's response, however, was almost immediate as they struck the woodwork for the second time in the match. Dragun fired towards goal from outside the box, and his effort was diverted against the underside of the bar by Nikoai Signevich from point-blank range.
The threat remained, and moments later they passed up another glorious opportunity to draw level as Aleksei Rios arrived unmarked at the far post and blasted a straightforward chance over the bar.
The goal had sparked the game into life and after Barkley had drawn a save from Scherbitski with a low drive, Davide Zappacosta forced the BATE keeper into another fine stop with a powerful header from close range.
As he had indicated in yesterday's pre-match press conference, Sarri withdrew Hazard just after the hour, the Belgian replaced by Willian, and another change quickly followed as Mateo Kovacic came on for Loftus-Cheek.
Barkley was unlucky not to get on the end of an inviting cross from Willian as we went in search of the second goal, and as the loose ball fell at the feet of Jorginho, the midfielder fizzed a right-footed drive just over the bar from distance.
We then broke forward at pace, with the numbers in our favour, but Pedro's pass to Willian was slightly over-hit, allowing Scherbitski to gather it a fraction ahead of the Brazilian.
Having only turned 18 yesterday, Callum Hudson-Odoi was introduced for the final eight minutes at the expense of Pedro, the youngster taking up a position on the left-hand side of the attacking trio.
Willian saw a late strike defelected behind as we attempted to wrap the game up, and Giroud then steered one wide at the near post, before BATE struck the woodwork for the third time right at the death.
Giroud's goal earlier in the half was enough, though, and the Blues, who remain unbeaten this season in all competitions, progress to the next stage of the Europa League.
Chelsea (4-3-3): Kepa; Zappacosta, Christensen, Cahill (c), Emerson; Barkley, Jorginho, Loftus-Cheek (Kovacic 64); Pedro (Hudson-Odoi 84), Giroud, Hazard (Willian 61).
Unused subs: Caballero, Azpilicueta, Ampadu, Kante
Scorer Giroud 52
BATE Borisov (4-3-3): Scherbitski; Rios, Volkov, Filipenko, Filipovic; Baga, Dragun, Hleb (Berezkin 80); Skavysh (Moukam 75), Signevich (Tuominen 72), Stasevich (c)
Unused subs: Chichkan, Yablonski, Ivanic, Polyakov
Referee Nikola Dabanovic (MNE)