Given that chance, he won 13 games for the American League West champions and convinced Rangers manager Ron Washington that he deserves a start in the AL Division Series.
Hunter gets that start in Game 4 at noon CT on Sunday, when the Rangers attempt for the second time to eliminate the AL East champion Rays, who notched a come-from-behind 6-3 victory on Saturday at the Ballpark in Arlington.
Texas leads the series, 2-1.
"I don't know [which team has the most pressure]," Hunter said after Saturday's game. "I really don't want to put pressure on anybody or have pressure on us or anything like that because it's a baseball game.
"We're going to go out and play like the little kids that we are, and just let things fall into place as they should."
The regular season fell into place for Hunter after he recovered from an oblique injury suffered in Spring Training.
He was sent to Triple-A Oklahoma City -- and didn't come back until June.
He admitted to being worried about getting buried.
"I just needed a chance," he said. "If I got a chance, I was hoping I could stay. That's all you can do. You just hope you can get a shot like the year before and the year before and take it from there."
He took the chance and ran with it, posting a 13-4 record and 3.73 ERA in 23 appearances, including 22 starts.
He credited the Rangers' defense and run support for his success, commended the catchers for calling the right pitches and pitching coach Mike Maddux for leading the way.
TOMMY HUNTER OF LATE ...
|Oct. 1||vs. LAA||5||3||1||L, 5-4|
|Sept. 24||at OAK||5.1||6||1||W, 10-3|
|Sept. 19||at SEA||6||6||2||L, 2-1|
Truth is, he had a lot to do with it himself.
What was better about this season?
"My strike percentage was a little better," he said. "My first-pitch strikes improved. I gave up a lot of home runs , so that's the biggest thing I need to improve. I need to make sure I find the bottom third of the strike zone.
"Overall, I had pretty good command of my fastball and that's what really helped me out."
More than anything, however, was opportunity.
"Just give me a chance and that's what they are doing," he said. "That's the only thing you can ask people to do. They believe in me and are giving me a chance. Now you have to prove yourself and make sure your name stands out the next time this comes up."
TOMMY HUNTER VS. RAYS
|June 5||vs. TB||9||5||1||W, 6-1|
|Aug. 17||at TB||3||6||4||L, 10-1|
His name comes up on Sunday, in the biggest game of his career.
Washington decided to go with a four-man rotation in the Division Series, primarily because he didn't want to pitch ace left-hander Cliff Lee on three days' rest.
"If we felt we had some type of advantage bringing Cliff Lee back in three days, [Hunter] would stay in the bullpen," Washington said.
And Hunter was the obvious choice as the Game 4 starter.
"He won us 13 games," Washington said. "That's enough reason right there."
Jim Street is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.