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Maurizio Sarri says Olivier Giroud is "very important" to Chelsea after the forward's first goal since May put the Blues into the last 32 of the Europa League.
The France international, who had not scored under Sarri, headed in Emerson's cross at the near post early in the second period to maintain the Blues' 100% Group L record.
"I'm pleased for him," Sarri said. "I know strikers want to score. And so for his confidence, I think it's very important.
"I don't want him to be worried about scoring, because for us he's very important, a very, very useful player for the team."
Chelsea are now six points clear of Hungarian side MOL Vidi, who moved up to second in the group with a win over PAOK Salonika.
Despite the chilly conditions in Belarus, a white-hot atmosphere had greeted Sarri's side at a tightly-packed Borisov Arena.
And it was the hosts, who had confirmed their 13th consecutive Belarusian league title on Sunday, who initially went on the offensive.
During a 60-second period, Bate twice carved out opportunities with Dmitri Baga's rasping drive hitting the post and Chelsea keeper Kepa Arrizabalaga athletically saving Stanislav Dragun's header from a corner.
But as Chelsea grew more assured, the hosts retreated, and Giroud finally registered his goal.
That prompted a strong response from Bate who created a glut of chances to level.
But Nikolai Signevich struck the left post, Aleksey Rios blazed over and Baga again hit the post from close range as the Blues held on to win.
Despite France's exploits in winning the World Cup in Russia in the summer, it was hardly a vintage tournament for Giroud who ended it without registering a single shot on target in 546 minutes of action.
And the prospects of an early-season pick-me-up were hardly assisted by his late return to training six days before the Premier League campaign started.
As a consequence, the 32-year-old has struggled for sharpness and to integrate into a style of play that is evolving under Sarri.
However, in his 12th match of the campaign and 794 minutes from his last goal in Chelsea colours, against Liverpool on 6 May, Giroud made a decisive contribution.
Tellingly, the 6ft 3in forward delivered it with a textbook downward header from Emerson's pinpoint left-wing cross to underline the value his aerial prowess offers in tight games.
While Sarri made seven alterations to the Chelsea team that defeated Crystal Palace 3-1 on Sunday, Eden Hazard was his most notable inclusion.
The Belgium international had missed three matches with a back problem before being introduced from the bench against Palace.
And this appeared the perfect opportunity for Sarri to give Hazard a match-sharpening run-out ahead of their weekend fixture against Everton.
The 27-year-old, making his first start in the competition, was given just over an hour and, in truth, struggled, perhaps justifying Sarri's desire to put more minutes into his legs.
Though Chelsea enjoyed almost 74% of possession, Hazard was largely anonymous, making 46 passes and touching the ball 65 times before he was withdrawn.
Ross Barkley helped Chelsea control possession with 94% passing accuracy from 113 passes
Chelsea manager Maurizio Sarri: "I think the first target in this competition was to qualify and now the second target is to win our group, so I think we need one more point [to top the group].
"It's very important because then we can talk again about this competition in February, when we will have another target."
What's next?
Chelsea return to domestic action on Sunday 11 November when they host Everton in the Premier League (14:15 GMT). The Blues host PAOK Salonika in their next Europa League fixture on Thursday 29 November (20:00 GMT).
Bate Borisov travel to Shakhtyor in the Belarusian league on Wednesday 21 November (15:00 GMT). They return to Europa League action on Thursday 29 November when they host MOL Vidi (17:55 GMT)
