Rangers starter Derek Holland (0-1) left after only one inning because of tightness in left shoulder, and outfielders Shin-Soo Choo and Ryan Rua also made early exits because of injuries.
Collin McHugh (1-0), who was 7-0 with a 1.77 ERA his final 10 starts as a rookie last season, struck out four and allowed one run over six innings.
Lowrie hit a solo homer in the first off Holland. Rasmus had a two-run shot in the ninth of closer Neftali Feliz pitching in a non-save situation.
No. 9 hitter Jake Marisnick had three of Houston's 10 hits and drove in two runs. The Astros totaled only three runs and eight hits in their season-opening, three-game series against Cleveland.
The Rangers said Holland felt the tightness in the back of his shoulder on the last pitch he threw during warmups. The team said the problem was in a different area than the shoulder soreness that slowed him early this spring after missing most of last season recovering from left knee surgery.
Anthony Bass took over then the second, and allowed one run in five innings. The right-hander had a defensive gem in the fifth when he had a diving backhanded stab to catch Robbie Grossman's popped-up bunt and turned that into a double play.
Right fielder Choo left after two innings because of spasms in his upper back, and Rua departed after five innings with a sprained right ankle sustained running into the left field corner chasing a ball.
Jose Altuve, the reigning major batting champion off to a 2-for-16 start this season, had a single on the first pitch of the game. But he was picked off second base by Holland just before Lowrie's second homer of the season. Lowrie's ninth-inning home run a day earlier broke a combined no-hit bid by Cleveland.
Marisnick had an RBI double in the fifth, and an RBI single two innings later after Grossman doubled.
Adrian Beltre had a double in the sixth and scored on a grounder by Delino DeShields, who had replaced Rua.
Astros: RHP Brad Peacock, who is rehabbing after hip surgery, allowed no hits in 4 2-3 innings in a start for Triple-A Fresno. He walked five batters and hit another one. "It's good that he was hard to hit," Houston manager A.J. Hinch said. ... RHP Josh Fields (right groin) threw live BP in Kissimmee, Florida, and next will pitch for Fresno, likely this weekend.
Rangers: RHP Tanner Scheppers (right ankle) struck out all three batters he faced for Double-A Frisco. The next step is pitching in consecutive games, which is the plan Saturday and Sunday.
Astros: RHP Roberto Hernandez, who went to spring training on a minor league deal after pitching last year for Philadelphia and the Los Angeles Dodgers, makes his Houston debut. The 2010 AL All-Star with Cleveland was 3-0 in his five spring training games to earn a rotation spot.
Rangers: Yovani Gallardo is from Fort Worth, and was acquired by Texas in January. The right-hander, who lost the season opener at Oakland, makes his home debut for the Rangers.