Santana (8-8) went the distance, scattering seven hits, walking one and striking out two for the Angels, who won their third straight division title and their fifth in the last six seasons.
Morales drove in two runs with his 33rd home run of the season in the first inning, when the Angels scored three runs. Vladimir Guerrero, Maicer Izturis and Erick Aybar each drove in two runs and Bobby Abreu and Torii Hunter each drove in one for the Angels, who came into the four-game series with the Rangers needing one victory to clinch the division crown.
Texas trails the Boston Red Sox by six games in the AL wild-card chase, with both teams having six games left to play.
Michael Young and Ian Kinsler had two hits apiece for the Rangers.
Texas starter Tommy Hunter (9-5) lasted just 2 1/3 innings, allowing seven runs on seven hits with two walks and one strikeout.
The Angels included their late teammate, Nick Adenhart, in their post-game clubhouse celebration, pouring champagne over his No. 34 jersey. The entire team then went to Adenhart's picture on the outfield wall for another moment of tribute to the rookie pitcher who, at age 22, was one of three people killed in a car crash in Southern California April 9, hours after his first 2009 appearance for the Angels.