For Chelsea this was mission accomplished with two games still to play, though Maurizio Sarri’s constant agitation on the touchline was more reflective of everything offered up by his team in the freezing fog of Borisov.

This side remain unbeaten under his stewardship, which feels mildly remarkable given it is approaching mid-November, and have qualified for the new year’s knockout in this competition. So it says everything about the perfectionist in Sarri that he still cut a distinctly dissatisfied figure even in victory.

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He could point to Olivier Giroud’s first club reward since the first week of May, a distant 794 minutes of scoreless football previously, as a positive in the murk. The World Cup winner’s reward, pilfered with a near-post header from Emerson Palmieri’s centre, will be a fillip given that Álvaro Morata has flickered back into life of late. Chelsea will need options for the fixture pileup ahead.

Yet the reality was that, while Bate Borisov only ever enjoyed the ball in fits and starts, the home side rattled the woodwork three times and missed other opportunities where it seemed easier to score.

The visiting players greeted the final whistle with relief, though the head coach refused to disguise his frustration at what he had witnessed, most noticeably when berating Eden Hazard for an overhit free-kick just after half-time. Perhaps his mood had been soured by the fever with which he had been suffering all day, a bug having presumably done the rounds at Cobham having already ruled Cesc Fàbregas out of this trip, but the only positive he could spy was the result.

“We didn’t play very well,” he grumbled. “I didn’t like the first half because we moved the ball only horizontal and slowly, so it was really very difficult to be dangerous. So the best situation this evening is the result. It wasn’t very easy to play a good game here. The conditions were very bad: the cold, the opponents, the pitch, everything. But, I think, we could still have done better.”

Facebook Twitter Pinterest Eden Hazard, making his first start for three weeks, evades BATE’s Dmitri Baga. Photograph: Darren Walsh/Chelsea FC via Getty Images

It was the rather aimless nature of the possession that had infuriated him, nullifying Chelsea’s intent and inviting pressure as it did when Bate found some rhythm of their own on the counter.

The approach play was busy enough when the visitors did whip up some tempo but the final pass invariably fizzled out in anticlimax. Davide Zappacosta threatened down the right, and Hazard’s close control was still a marvel on his first start in almost three weeks after back trouble, but the visitors did not muster a single effort on target in the opening period, the first time they had endured such indignity under Sarri.

The pitch and the fog, rolling in out of the dense forests around Borisov, did not help but even the Italian admitted the inhospitable conditions were no excuse.

At least they summoned one moment of quality to squeeze out a lead. It was Emerson, far more convincing as a forward thinker than a defender down the left, who supplied the first accurate cross of Chelsea’s night early in the second half with Giroud leaping to connect at the near-post.

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The France international’s header bounced down and up over Denis Scherbitski’s attempt to save, and Chelsea had the advantage they had craved. “I came back late from the World Cup and I was lacking maybe a bit of efficiency and luck,” said Giroud. “But you always need to keep working hard and keep the faith.”

It was good fortune that arguably kept them in it thereafter. Dmitri Braga had already left the post quivering, startling Kepa Arrizabalaga with a shot that swirled out of the mist. Nikolai Signevich would deflect Stanislav Dragun’s optimistic shot on to the crossbar in the aftermath of Giroud’s goal, with the substitute Evgeni Berezkin repeating Braga’s trick in stoppage time at the end.

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Throw in Kepa’s smart save from Signevich’s header and a horrible miss from Aleksei Rios, looking every bit a right-back, and the distinctly uncomfortable nature of Chelsea’s evening was very evident.

“They could have drawn the match,” added Sarri. “Bate played very well. But now we have the target to win the group.”

A point against either Vidi or PAOK will now secure Group L. That achievement is to be anticipated given Chelsea’s status. But the head coach will expect his team perform far more coherently than this in the two European fixtures to come.