Neftali Feliz made things interesting in the ninth inning after entering with a three-run lead, allowing the tying run to come to the plate with no outs, but he reared back and closed out the Rangers' 4-2 victory at Boston.
Elvis Andrus snapped out of an 0-for-26 slump to go 3-for-4.
The Rangers took three of four at Fenway in their first series after the All-Star break. The only loss was the extra-inning affair in which Cliff Lee allowed two runs in nine innings.
They head to Detroit to start a three-game series Monday before coming home for four games against the second-place Angels, who trail Texas by four games pending the outcome of their game Sunday against Seattle.