But Rangers starter Eric Hurley walked two in three hitless innings.
He was a first-round selection and was named the Nolan Ryan Minor League Pitcher of the Year in 2006, but has missed the past two seasons because of injuries. He missed all of 2009 after right-shoulder surgery and missed 2010 with three wrist injuries.
"The goal is to make the team," Hurley said. "I got out of bad counts and back into counts with my fastball."
Rangers manager Ron Washington said he was impressed.
"He battled out there today," Washington said. "It's rewarding, especially for him not pitching for two years."
The Angels broke a scoreless tie in the sixth off Ryan Tucker. Peter Bourjos opened with a single and then scored on Maicer Izturis' double into the right-field corner.
They extended the lead to 2-0 in the seventh when Mark Trumbo opened with a single and took second on right fielder Engle Beltre s field error. Trumbo scored on Jeff Mathis' squeeze bunt.
Ervin Santana, in line to be Los Angeles' third starter, could be a key part of one of the majors' best rotations.
"(We're) better than anybody, to me," said Santana, who was then asked to compare with Philadelphia's impressive five headed by Roy Halladay and Cliff Lee.
"They're human," Santana said. "They have more experience, OK?"
Texas' Jose Ruiz doubled and scored the only Rangers' run in the ninth.