Hunter scattered nine singles over seven-plus innings on his 24th birthday and Texas beat the Chicago White Sox 3-1 on Saturday night.
Hunter (5-0) allowed one run, struck out three and walked one for the AL West leaders to lower his ERA to 1.98.
The right-hander sustained a left oblique strain in spring training and began the season on the disabled list. After recovering, he made six starts for Triple-A Oklahoma City before he was called up on June 5.
Texas, which has lost three starters to injuries at various times this season, has won all six games Hunter has started in 2010.
"Pound the strike zone, not make mistakes in the middle of the plate, executing, keeping the ball in play, doing everything you like a pitcher to do," Rangers manager Ron Washington. "When you don't have overpowering stuff, that's what you do."
Hunter's outing included a three-pitch sixth inning against an aggressive lineup.
"I've never done that," Hunter said. "I was very pumped about that."
Hunter, who has gone at least six innings in five of his six starts this season, left in the eighth to a standing ovation after Juan Pierre drew a leadoff walk and Alexei Ramirez singled for his third hit of the night.
The runners moved up on Frank Francisco's balk, and Pierre scored on Alex Rios' groundout.
But Francisco struck out slugger Paul Konerko and retired Andruw Jones on a fly ball to preserve the two-run lead.
Chicago's first nine hits were singles until pinch-hitter Brent Lillibridge's leadoff double in the ninth against Darren Oliver. Neftali Feliz struck out pinch-hitter Carlos Quentin and Gordon Beckham for his 23rd save in 24 chances.
"(The Rangers) are pitching pretty good," White Sox manager Ozzie Guillen said. "That's the reason they're in first place."
White Sox starter John Danks (7-7) gave up two runs and four hits in six innings. He struck out four and walked four.
"I got outpitched," Danks said. "Tommy Hunter was good today. You've got to tip your hat to him for sure. I would have liked to have walked less than I did. But I kept the ball in the ballpark and gave us a chance to win."
Danks' teammates have provided three runs or fewer in 10 of his 16 starts this season.
Chicago, which had won 17 of 21, is two games out of first place in the AL Central.
Josh Hamilton extended his home hitting streak to 23 games with a second-inning infield single. Hamilton is tied with Michael Young (2009) and Ivan Rodriguez (1995) for the second-longest home streak since the team relocated from Washington in 1972.
Al Oliver's 30-game run in 1981 is the club's longest at home.
Later in the second, Joaquin Arias' groundout drove in Hamilton from third with the game's first run. Elvis Andrus made it 2-0 in the fifth when his single scored Arias from second.
The Rangers stretched their lead to 3-0 in the seventh when Nelson Cruz scored from third while pinch-hitter Justin Smoak was grounding into a double play.
NOTES: Hamilton was officially credited with the longest home run in the 17-year history of Rangers Ballpark after research by a college physics professor concluded that his drive June 27 against Houston traveled 490 feet. The original estimate by the Rangers was 468 feet, but Andrew Brandt of Texas-Arlington -- in consultation with other experts -- calculated the longer distance. Jose Canseco held the previous record at Rangers Ballpark, a 480-foot shot for Texas in 1994. ... Hamilton hit into his first double play of the season in the sixth. He'd gone 308 at-bats without one. ... Smoak was replaced at 1B in the starting lineup by Arias. Smoak, who had started 61 of the previous 64 games at 1B, is in an 0-for-20 slide. ... Rangers RHP Rich Harden threw another bullpen session in his rehab from a strained gluteal muscle. Harden will need at least one more bullpen session, then throw batting practice before a minor league rehab start. ... Quentin wasn't in the starting lineup as Guillen gave his everyday RF a break after Quentin was hit by a pitch on Friday night. Jones got the start in RF and went 0 for 4.