The Rangers managed only one run on eight hits over the first three innings, but broke things open with a five-run fourth. Boston had won its previous two games and came into the contest with the best record in baseball.
Holland (3-2) gave up six hits and walked one while throwing 112 pitches. Derek Lowe worked a perfect ninth to preserve the shutout.
Texas came up with four two-out hits in the fifth inning to take control. Elvis Andrus drove in one run with a single, Adrian Beltre produced a three-run double and Nelson Cruz singled in the final run of the frame.
Felix Doubront (3-1) suffered the loss after being torched for six runs on 12 hits in just 3 2/3.
Texas had dropped four of its previous five games and was coming off its first lost series of the season against the Chicago White Sox.
Swim Week Miami Beach 2014 [PHOTOS]