Chavez, who spent nearly two years recovering from knee surgery, had four hits to help Texas overcome a three-run deficit to beat the Cleveland Indians 7-4 Thursday night.
"I'm happy to be back," said Chavez, whose ninth four-hit game tied a career high and gave him a .415 (17 of 41) average since being recalled from Triple-A Round Rock on May 14.
"He's playing the way he did before he got hurt," Texas manager Ron Washington said. "He did so much rehabbing and is reaping the rewards."
Michael Kirkman (1-0) earned his first career win. The left-hander allowed one run over three innings in his 18th career relief outing. Neftali Feliz pitched the ninth for his 12th save in 15 chances.
"That was very exciting," Kirkman said. "I think every kid dreams of winning in the big leagues. Hopefully there's a lot more to come."
Cleveland dropped to 19-7 at home and has lost three in a row at Progressive Field for the first time this year as Carlos Carrasco (4-3) couldn't hold a 3-0 lead. The Indians went 2 for 12 with runners in scoring position, twice making three straight outs with two runners on base.
"We didn't swing the bats particularly well," Indians manager Manny Acta said. "We didn't pitch very well and we didn't play very good defense either."
The Rangers twice scored on errors and totaled 12 hits. Chavez, batting ninth, provided the offensive impetus with his speed. He had an RBI triple and scored in a three-run sixth that put Texas ahead 6-3. He also had a line single and stolen base in a three-run fifth, and added two infield hits, the last on a well-placed bunt.
The last time the speedy outfielder had four hits was on July 25, 2008, for the New York Mets. The next June, playing for Seattle, he tore a ligament in his right knee. He signed with Texas before the 2010 season, but was limited to just eight games in the minors.
"I had my doubts," Chavez admitted about making a comeback. "It was tough. I had to stay strong (mentally) and I thank the Rangers for their support."
Bush started in place of left-hander Matt Harrison, who has a blister on the middle finger of his pitching hand.
"Bush went out and gave us everything he had," Washington said. "Kirkman did what we needed, too, and it worked out for us."
Held to one hit over four innings, the Rangers tied it at 3 in the fifth. Cruz doubled, moved up on one groundout and scored on another. Chavez then singled and after Ian Kinsler walked, Elvis Andrus and Josh Hamilton each lined two-out RBI singles.
With one out in the sixth, Cruz doubled to left. He went to third on a single by Mitch Moreland and scored on a sacrifice fly by Torrealba to put the Rangers ahead 4-3. Chavez then tripled home Moreland. With Kinsler at-bat, Carrasco threw a pitch past Carlos Santana, who recovered in time to freeze Chavez coming down the line. Santana's throw to Carrasco covering the plate was wild and had to be tracked down by third baseman Hannahan. His throw back home was to late to get the speedy Chavez, who slid in ahead of the tag by Carrasco.
"I didn't think it went far enough away to go," Chavez said. "Then he threw back and there was nobody there so I just took off and made it."
Matt LaPorta opened the Indians' seventh with his eighth homer, a 422-foot shot into the bushes past the center field wall.
Carrasco, seeking to win his fourth straight start, gave up five earned runs over six innings, failing to get a strikeout.
Texas did not strike out for the first time since May 31, 2008. ... The Rangers have won eight of their last nine games in Cleveland. ... Moreland has hit .500 (13 of 26) over his last eight games. ... Texas had two stolen bases, one night after getting five in a game for the fourth time this year. ... Washington said he expects Harrison to make his next start Tuesday against Detroit. ... Rangers coaches Mike Maddux and Gary Pettis are not with the team. Both are attending their children's high school graduations. ... Acta used Grady Sizemore at DH. He wanted to give the outfielder, who has had problems with both knees, a break after Sizemore played on artificial turf in Toronto earlier this week. ... Cavaliers guard Baron Davis and pro wrestling star Jerry (The King) Lawler participated in first-pitch ceremonies.