The Orioles captured the opener 6-5, with all five of their hits in that contest being homers, but Texas won three of the four games in the series.
Josh Hamilton, who Tuesday became the 16th player in major league history to hit four home runs in a game, added another one for Texas in the first inning of Thursday's nightcap. Six of his 15 homers this year came in this series.
Baltimore scored three unearned runs in the second thanks to the three errors committed by Texas in the inning, but the Rangers regained the lead in the fifth when Mike Napoli tripled home Nelson Cruz and then scored on the single by Andrus.
Andrus had an RBI base hit during a three-run seventh.
Derek Holland (3-2) gave up four hits without an earned run in six innings to get the victory.
Tommy Hunter (2-2), recalled from Class AAA Norfolk to make the start, surrendered four runs on five hits in six frames. He walked one and struck out seven.
The doubleheader was made necessary by a rainout Wednesday.
Celebrity Families of 2014 [PHOTOS]