However, Moses came off the bench to head in Juan Mata's corner in the third minute of injury time to seal a dramatic triumph for the Blues.
© PA Photos
Chelsea went ahead in comical circumstances after only six minutes as Torres charged down Shakhtar goalkeeper Andriy Pyatov's clearance before finding the net.
However, they were ahead for only five minutes when Willian calmly struck the ball through a number of Chelsea players to get Shakhtar level.
Despite the away side's dominance, Chelsea regained the lead five minutes before half-time when Oscar lobbed Pyatov from all of 40 yards after the goalkeeper had come out of his area to head the ball clear.
It took Shakhtar only a minute after the break to equalise and it was Willian again who showed composure to slot the ball past Cech at his near post.
Razvan Rat nearly gave the Ukrainians the lead moments later, but his stinging effort came back off the post.
Jon Obi Mikel rightly had his header ruled out for offside just after the hour before the midfielder shot narrowly wide.
The game looked to be heading for a draw when Moses came off the bench to nod in Mata's corner and earn the three points for Chelsea.