The substitute nets late winner with the last touch of the game after the Blues were twice pegged back by the Ukrainian champions in a thrilling encounter at Stamford Bridge
The substitute rose high in the last minute of added time to head home Juan Mata's corner at the end of a thrilling encounter in which the Blues twice took the lead but made poor defensive errors as they were pegged back by the swift attacking movement of the Ukrainian champions.
Shakhtar playmaker Willian - a transfer target for Chelsea and Tottenham - twice equalised for the visitors to cancel out Fernando Torres' sixth-minute goal and a wonderful 45-yard strike from Oscar.
But Moses had the final say with a goal that leaves Chelsea alongside Shakhtar on seven points, a step closer to qualification with two games to play - at home to Nordsjaelland and away to Juventus.
It was a victory that Chelsea barely deserved against a lively, creative Shakhtar side who continually took advantage of the hosts' sloppy defending, which will prompt questions over whether manager Roberto Di Mattero should have recalled captain John Terry to the side. The Italian cited the defender's lack of match sharpness following his racism ban for the decision to start with Gary Cahill and David Luiz as his centre-back pairing.
Shakhtar named the same side who won the reverse fixture 2-1 in October and the game burst into life from virtually the first kick, with both teams mixing swift attacking play with almost comical defending.
Given Torres' struggles to score in his Chelsea career, the early gift from Shakhtar goalkeeper Andriy Pyatov will have been warmly received. The Ukrainian received a routine backpass from Yaroslav Rakytiskyy but Torres read the clearance and opportunistically stuck out a leg for the ball to ricochet straight into the net.
Three minutes later, however, the Ukrainian visitors were level as Fernandinho burst past Chelsea defenders into the right side of the penalty area and cut the ball back for fellow Brazilian Willian to slot through a crowd of bodies, with Petr Cech diving the wrong way.
The game then settled down but never lost its ebb and flow as both sides created chances. Torres could only find the side netting from a tight angle before Alex Teixeira zipped an effort just wide of the post following a flowing Shakhtar move.
Five minutes before the break, Chelsea once again took the lead thanks to a wonderful strike from Oscar and another woeful clearance by Pyatov. The keeper rushed off his line to clear Mata's through-ball with his head, only to supply the Brazilian. The playmaker still had so much to do but made it look effortless, controlling with his chest before pinging his finish into an empty net from 45 yards.
The fluid, end-to-end pattern continued after the break and Willian again levelled the score in the 47th minute as he side-footed Dario Srna's cross with his left foot to finish a wonderful Shakhtar move.
The Ukrainian champions nearly took the lead seven minutes later but Razvan Rat saw his swerving strike from 30 yards rattle the post.
At the other end, Chelsea had a huge shout for a penalty when Ramires appeared to be brought down in the area by Srna as he shaped to shoot, only for referee Carlos Velasco Carballo to wave away the appeals to the home players’ astonishment.
Then, with the last touch of added time, Moses rose in the box to head home Mata's corner to send Stamford Bridge into delirium.