Chelsea had led twice, only for Shakhtar to reply on both occasions through Willian, as the Ukrainian champions threated to inflict more misery on Roberto Di Matteo's side after their 2-1 win in Ukraine two weeks ago.
However, Moses' goal enabled Chelsea to draw level with Shakhtar on seven points in Group E, giving them a one-point advantage over third-placed Juventus.
United progress Braga: Manchester United became the first British side through to this season's Champions League knockout stage after coming from behind to beat Group H rivals Braga 3-1 on Wednesday.
Needing just a point to assure their qualification to the last 16, United fell behind to a penalty from Alan just after half-time but strikes from Robin van Persie, Wayne Rooney and Javier Hernandez ensured the Red Devils maintained their perfect record in this year's competition.
But the game was interrupted only a few minutes later as a generator broke down, leaving the stadium shrouded in darkness and the players ordered back to the changing rooms.