Kenny Miller took advantage of calamitous Celtic defending to fire Rangers into a two-goal lead and Aiden McGeady's penalty failed to trigger a comeback.
Sutton then got in behind the Celtic defence to fire in a shot that was comfortably held by Mark Brown, the goalkeeper included in place of Artur Boruc, who is awaiting knee surgery.
United continued to press, but Celtic killed off their challenge when Majstorovic dived low to fire into the near corner of the net from Mulgrew's free-kick to the front post.