Martinez smashed a three-run homer with one out in the ninth inning Tuesday night, giving the Tigers a 4-2 victory over the Indians.
The pitch from Cleveland closer Cody Allen (5-4) landed in the trees in straight-away center field, 418 feet from home plate, scoring Hunter and pinch-runner Steven Moya.
It was Martinez's second home run in three career at-bats against Allen, both of which occurred this season. He went 3-for-5, upping his season average in the ballpark to .464 with five homers and 13 RBIs.
"It was one of those swings that feels perfect, like you couldn't have done anything better," said a beaming Martinez, who has a career-high 19 home runs. "When I reached home, I was so pumped up, I wasn't sure if I had touched all the bases.
"It's September, this is win-or-go-home time. I'm so excited because I want to make the playoffs for the first time so bad."
The Tigers maintained a 1 1/2-game lead over the Mariners in the race for the second American League Wild Card. Detroit remained a half-game back of Kansas City in the AL Central.
Reliever Phil Coke (3-2) earned the win with 1 1/3 scoreless innings, while closer Joe Nathan worked the ninth for his 29th save in 35 chances.
"Fortunately, our pitching held the Indians at bay long enough for us to make a comeback," Detroit manager Brad Ausmus said. "We strung together some hits against a very good closer."
Hunter drew a walk off Allen to start the frame, while Miguel Cabrera followed with a sharp single up the middle. After Victor Martinez flied out, J.D. Martinez played the role of hero as the Tigers improved to 5-54 when trailing entering the ninth.
"I didn't make the pitches when I had to, fell behind, and had to throw hittable pitches to good hitters," Allen said. "They didn't miss them. J.D. Martinez got extended on a fastball and hit it real hard."
Cleveland entered the ninth with a 2-1 advantage, thanks to a Carlos Santana two-run homer in the first off Detroit left-hander Kyle Lobstein. The rookie struck out a season-high 10 in 5 1/3 innings, scattering five hits after being recalled from Triple-A Toledo before the game.
Lobstein made his Major League debut in relief Aug. 23 at Minnesota, then went six innings in his initial start on Aug. 28 against the Yankees. Ausmus said the lefty will remain in the rotation and pitch Sunday against San Francisco.
"I struggled with my command early and gave Santana that good pitch to hit, but I put it out of my mind after that," said Lobstein, who has a 3.18 ERA over three appearances and 17 innings. "I'm just trying to eat up some innings and prove that I deserve to be out there every five days."
The Tigers scored their first run in the second, when Indians right-hander Carlos Carrasco walked Alex Avila with the bases loaded, plating Victor Martinez.
Carrasco struck out a career-high 10 and allowed 10 hits in 5 1/3 innings, but rose to the occasion when he needed to in stranding 10 runners.
"We knew what he was going to throw, but we couldn't hit it," Hunter said. "Big ups to him."
Cabrera, Victor Martinez and Rajai Davis joined J.D. Martinez with three-hit games for Detroit, which has taken the first two contests in the four-game series.
Avila exited in the sixth when he was struck squarely on the mask by a foul ball, but passed all of the medical tests after the game. Bryan Holaday replaced him behind the plate.
"It definitely rung my bell at the time," Avila said. "But I saw the doctor and I should be fine. I actually feel OK now. I'll be back out there as soon as I can."