Ortiz smacked a two-run double in the second inning, capping a four-run Boston uprising, and later added a sacrifice fly, extending a 19-game hitting streak stretching back to last season.
Doubront (3-0) went 6 2/3 innings to gain the decision, allowing four hits and three runs while racking up eight strikeouts to overcome four walks.
Jacoby Ellsbury knocked in a pair as the Boston recorded a third straight win over Houston.
Astros starter Brad Peacock (1-3) was roughed up for five runs on six hits, issuing five walks in a 3 1/3-inning effort.
Swim Week Miami Beach 2014 [PHOTOS]