Santana allowed one run and five over five innings Saturday, helping the Angels to a 3-2 victory in the first of back-to-back games between the division opponents.
"I don't try to change a thing," said Santana, who is 12-9 in 24 career starts against the Rangers. "I just stick to my routine and try to use all my pitches."
Santana walked two and struck out two. He allowed at least one runner each inning but held Texas scoreless until Ian Kinsler hit his third spring training homer leading off the fifth.
Harrison, whose regular turn in the rotation was Saturday, pitched in a minor league game on a back field. Japanese rookie Yu Darvish will pitch in an intrasquad game against Texas minor-leaguers Sunday rather than travel to Tempe to face Los Angeles.
Rangers starter Greg Reynolds started in Harrison's place and gave up one unearned run and two hits in five innings.
"He pitched well and kept the ball down," Texas manager Ron Washington said.
Texas first baseman Brad Hawpe, who is fighting for one of the final roster spots, hit his first home run, a drive leading off the seventh.
New closer Joe Nathan followed Reynolds and allowed two runs, three hits and a wild pitch in one inning. Nathan has given up eight runs and eight hits in five innings.
"He's my closer," Washington said. "My assessment of that is, get it out of your system now. The ball's coming out of his hand well. I know what he's capable of doing."
Harrison pitched six scoreless innings against Triple-A Omaha, allowing two hits and striking out four. ... Angels C Kendrys Morales went 1 for 3 with an RBI before a pinch-runner replaced him in the sixth. Morales, who has played three straight days after missing the entire 2011 season with an ankle injury, received a standing ovation from the many Angels fans in the sellout crowd as he returned to the dugout. ... Rangers RHP Neftali Feliz, who left his start Tuesday after three innings with stiffness in his right shoulder, threw 25 pitches off a bullpen mound and is to throw another bullpen session Sunday. ... All the Texas starters save center fielder Julio Borbon were given the afternoon off after the fifth inning.