The rookie showed Wednesday night that he can hit a little, too.
"I said that the kid was not going to be an out," Texas manager Ron Washington said. "We've got nine guys in our lineup who can get you. Elvis is not going to hit many home runs. But every now and then, he's going to catch one."
The 20-year-old Andrus, who is 3-for-8 to start the season, was in Double-A last season and he got the shortstop job before the season started. Five-time All-Star Michael Young moved to third base to accommodate Andrus.
The rookie showed off his defense in the opener Monday by starting two double plays.
Andrus homered off Rafael Betancourt in the sixth.
"I just hit it hard and started running," Andrus said. "At first I thought it was a triple. I saw the umpire signal [home run] when I got to second base."
Ben Francisco homered for the Indians, who have been outscored 17-6 by Texas in the series.
Cruz led off the second inning with a home run off Fausto Carmona (0-1), who allowed six runs and seven hits in five innings. Cruz added another shot off reliever Rafael Perez in the seventh that landed in the second level of seats in left.
"That's a good hitting club," Indians manager Eric Wedge said. "They've gotten some pretty good swings out there the last couple of days."
Vicente Padilla (1-0), the Rangers' win leader with 14 in 2008, allowed four hits and three runs in 5 2/3 innings to help the Rangers open 2-0 for the first time since 2000. Frank Francisco pitched a scoreless ninth for his first save.
"It's always good to start with wins," Cruz said. "Since spring training, everybody has talked about being together and supporting one another."
Coming off a 9-1 victory over American League Cy Young winner Cliff Lee on Monday, the Rangers scored four runs against Carmona in the second.
Cruz hit his first homer to left-center, and Texas then had four straight hits to build the lead.
Carmona is trying to rebound after missing two months last season with a left hip strain. After winning 19 games in 2007, Carmona was 8-7 with a 5.44 ERA in 2008.
"I don't really know what happened," said Carmona, who was 4-1 in the spring with a 2.67 ERA. "I just missed up on a couple of pitches."
Ryan Garko was hit by a pitch with the bases loaded in the fourth to bring Cleveland within 4-1.
Josh Hamilton, who led the American League with 130 RBIs in a breakout 2008 season, drove in his first run of the season with a triple in the fifth. Cruz added an RBI groundout to score Hamilton and make it 6-1.
Francisco hit a two-run homer in the sixth that chased Padilla.
Young and Andrus each made their first error of the season.
Young's came on an errant throw to first in the fifth inning, and Andrus had a throwing error which allowed an unearned run to score in the seventh.
Washington said Texas catcher Jarrod Saltalamacchia left the game in the eighth with inner ear inflammation that caused dizziness. With Asdrubal Cabrera at the plate, Washington helped his catcher off the field, and Taylor Teagarden came into the game.
Indians infielder Jamey Carroll, on the disabled list because of a broken bone in his left hand, will not undergo surgery. He's expected to miss 4-6 weeks. ... Washington said SS Omar Vizquel and Teagarden should make their first starts of the season in the series finale Thursday.