Hunter pitched a five-hitter in his season debut, and Josh Hamilton homered in the Rangers' 6-1 victory over the Rays on Saturday.
Hunter (1-0), called up from Triple-A Oklahoma earlier in the day, struck out four and didn't issue a walk. He retired 14 of the last 16 batters he faced for his second career complete game.
On an afternoon when field temperatures were over 100 degrees, Hunter threw 117 pitches, keeping the Rays off-balance with an effective cutter and breaking balls.
"It was hot," Hunter said. "There's nothing else to say. It was hot. They made sure I was OK. They asked me, 'Are you all right?' I said I'm good. They let me go out and finish the job."
Hunter began the season on the 15-day DL because of a left oblique strain he sustained in spring training, and he began a minor league rehab stint on April 28.
After going 1-2 with a 4.05 ERA in six starts for Oklahoma City, Hunter on Saturday assumed the rotation spot of left-hander Derek Holland, placed on the 15-day disabled list last Tuesday due to left rotator cuff inflammation.
Hunter's other complete game came against Seattle on Sept. 13, 2009.
Hunter's ability to work fast and get ahead of hitters is appreciated by teammates.
"I've always like played behind Tommy," Rangers third baseman Michael Young said. "He gets the ball and gets back on the mound and goes after guys. He trusts his stuff and he's out there trying to throw good pitches and he's aggressive in the strike zone. Those are the kind of guys you want to play defense behind."
Hunter kept his pitch count relatively low in the early innings, and that allowed him to finish the game.
"Having those easy pitch innings helped him get to the back of the game," Rangers manager Ron Washington said.
Hamilton continued his hot June with a two-run blast in the first, and is 10 for 22 this month to raise his average from .281 to .299.
Sean Rodriguez homered for the Rays, who've lost eight of their last 12 but maintained a two-game lead over the New York Yankees in the AL East.
The Rays have played sound fundamentally for most of the season, but they made two baserunning mistakes and two errors on Saturday.
"We did not play well today," manager Joe Maddon said. "It was not one of our better games. But if we win tomorrow, it'll be a 3-3 road trip and I'll be very happy with that."
Elvis Andrus, who had two hits and two RBIs, led off the first against James Shields (5-4) with a double. Andrus went to third on Shields' wild pitch, and scored when Ian Kinsler's hot grounder glanced off Evan Longoria's glove at third base for an error.
Hamilton's homer later in the first made it 3-0, with all three runs unearned.
Rodriguez's solo homer in the second pulled Tampa Bay to 3-1, but Andrus' RBI ground-out in the second restored Texas' three-run advantage.
Tampa Bay designated hitter Hank Blalock had a baserunning gaffe in the second that cost the Rays a run. Blalock doubled, then inexplicably took off for third and was tagged out. Rodriguez, the next batter, homered.
Julio Borbon's suicide squeeze bunt in the sixth drove in David Murphy, and Andrus' RBI triple extended Texas' lead to 6-1.
Shields gave up six runs -- three earned -- and 10 hits in seven innings, losing for the fourth time in his last five decisions.
Shields was still able to hang in, throwing 106 pitches in the heat despite a tough first inning.
"We were a little flat in the first inning," Shields said. "I gave up the knock to Hamilton and it went from there. We just couldn't get it going. Obviously, it was hot, 110 or something on the field. But we were prepared for it. This is the big leagues. This is what we're conditioned to do."