Mourinho rescued by Willian's bolt from the blue
Mourinho's tenuous hold on his job appeared to be loosening even further when Dynamo's Aleksandar Dragovic cancelled out his first half own goal with a late equaliser for the Ukrainian champions.
But with just seven minutes remaining at Stamford Bridge, Brazilian winger Willian whipped a sensational 30-yard free-kick into the top corner to give Chelsea just their second win in their last nine games in all competitions.
Failure to beat Dynamo would have left the struggling English champions in severe danger of failing to make the last 16, but Willian's heroics lifted them to second place in Group G and put qualification back in their own hands with fixtures against Maccabi Tel Aviv and Porto remaining.
Chelsea were still well below their best, yet the result will buy Mourinho time to work on resolving the crisis that threatens to bring a premature end to his second spell at the club.
"The win is a big relief. The players deserve to get compensation for their hard work," Mourinho said.
"Many players are coming to their normal levels, despite having feelings as a team when negative moments come.
"The difference today was we had confidence in the negative moment.
"The team was strong mentally, they kept trying and I'm happy with that."
Amid all the talk of a dressing room mutiny from a group of players unhappy at his stern man-management, the Portuguese coach continues to insist he won't be sacked and captain John Terry leapt to his defence on Tuesday in passionate fashion.
But it was deeds rather than words that would define the remaining days of Mourinho's reign and he made a big statement by dropping Eden Hazard after another poor display in Saturday's loss against Liverpool.
- Constant menace -
Chelsea quickly seized the initiative and Willian was a constant menace on the right flank, but when he whipped over a teasing cross no Chelsea player was alert enough to convert the chance, triggering an anguished cry from Mourinho.
Like most of his team-mates Diego Costa has been painfully short of his best this year and he shot wildly over when the ball fell to him inside the penalty area.
But Mourinho's luck changed for the better in the 34th minute as Chelsea took the lead in fortuitous circumstances.
Blues goalkeeper Asmir Begovic got away with a scuffed clearance towards Baba Rahman, who played a long pass from the left out to Willian on the right and he tricked his way past his marker before drilling a cross into the six-yard box.
Again Chelsea's forwards hadn't anticipated the delivery, but this time it didn't matter as Dragovic threw himself at the ball in an attempt to head clear but instead diverted it past Olexandr Shovkovskiy and into his own net.
After dominating the first half, Mourinho's men were far less dynamic in the second half and, after Ramires survived a Kiev appeal for handball, a sloppy pass from Nemanja Matic was almost punished by Junior Moraes' powerful strike.
Kurt Zouma should have settled Chelsea's nerves, but the defender somehow poked wide from close-range as he stretched to reach Willian's free-kick.
It took an excellent save from Shovkovskiy to deny Oscar at the end of a flowing Chelsea move when the Brazilian curled his shot towards the top corner.
Unfortunately for Mourinho, his own goalkeeper wasn't so sturdy as Chelsea were rocked by Kiev's 78th minute equaliser.
Begovic came to punch a corner but didn't connect as Matic glanced the ball away from him into the path of Dragovic, who lashed into the net.
That could have been the signal for Chelsea to crumble.
But Willian came to the rescue in spectacular fashion in the 81st minute when he curled his free-kick into the top corner to spark wild celebrations in the stands and a sigh of relief from Mourinho.