The English champions bossed the game throughout a largely one-sided first half and led at the break after Dynamo centre back Aleksandar Dragovic headed into his own net after 33 minutes.
The same player then scored at the right end when he thundered in Dynamo's equaliser after 77 minutes as the visitors battled their way back into the match.
Willian, however, stepped up to strike a brilliant free kick from 25 metres that left Dynamo keeper Olexandr Shovkovskiy flailing and with no chance of saving.
The result put Chelsea in second place on seven points, behind leaders Porto on 10. Dynamo have five points and Maccabi Tel Aviv none.
Despite the depressed mood surrounding Chelsea following their miserable start to the season, the home fans still sang the name of under-pressure manager Jose Mourinho, who recognised their support by waving to all parts of the stadium.
"The win is a big relief. The players deserve to get compensation for their hard work," Mourinho told BT Sport.
"The difference today was that we had confidence in the negative moment. The negative moment is always arriving for us.
"I think the team was strong mentally, they kept trying and I'm happy with that."
The Chelsea boss was noticeably happier than he had been during their defeat to Liverpool at the weekend.
He even burst into laughter on occasion, most theatrically when Czech referee Pavel Kralovec waved away appeals for a penalty after Diego Costa was sent tumbling just before halftime.
TV replays showed the official's decision was correct, but Chelsea deserved their halftime lead after dominating possession.
Willian caused the Kiev defence problems on the right every time he had the ball and it was his cross that led to Dragovic's own goal.
Kiev, who had kept 14 clean sheets in 19 matches coming into the game, defended superbly with Yevhen Khacheridi and Dragovic dealing with almost everything Chelsea threw at them.
Dynamo came into the game more after the break and Artem Kravets was denied a shot on goal by a brilliant tackle from Kurt Zouma.
Substitute Junior Moraes then forced Asmir Begovic into an acrobatic save with a powerful drive just after replacing Kravets in the 57th minute.
Zouma had a great chance to double Chelsea's lead three minutes later but somehow skewed the chance wide following a Willian free kick.
Chelsea never regained the dominance they displayed in the first half but found an extra gear to grab the winner after Dragovic's leveller, keeping their chances of qualifying for the last 16 intact.
(Reporting by Mike Collett; editing by Toby Davis)
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