The Ukrainian champions, who had been unbeaten in 18 matches in all competitions this season, seemed set for a well-deserved point at Stamford Bridge when Moses rose unmarked at a corner to score.
The goal immediately transformed Chelsea's chances of qualifying for the knockout round, moving the Londoners on to seven points in Group E - the same as Shakhtar. Juventus (six) follow with FC Nordsjaelland on one with two games remaining.
NEWSLast-gasp Moses header snatches Chelsea win
"I think in terms of the timing of the goal you could agree there was an element of luck because it was the last action of the game but when you get a win against such a good team as them you deserve it," Chelsea manager Roberto Di Matteo said.
"It was a game we needed to win and we achieved that under a lot of pressure. We need to get something out of our last games now."
"It was a pity that today we unfortunately had a goalkeeper who made some mistakes and that cost us.
"He knew what to do on the last goal... he knew very well what I asked him to do before the game. I told him to stay within the six metres.
"He forgot at the last moment. I am very angry it was a lack of concentration and lack of experience, something went there."
Shakhtar had looked the better team for long periods with midfielder Willian running the match with an inspired performance as he scored both of Shakhtar's goals and left Chelsea's players trailing in his wake.
Shakhtar were level three minutes later when Willian side-footed home from close range after Fernandinho made a powerful run through the fragile left side of Chelsea's defence where youngster Ryan Bertrand had a torrid time.
The goalkeeper, out of his penalty area, for some reason decided to head the ball instead of kicking it. The header went straight to Oscar, who fired a perfectly struck 35-metre shot over Pyatov's head and into the net.
