Aubrey Huff, who has slumped since being acquired from Baltimore Aug. 17, added three RBIs for the Tigers, who won their second straight.
Jackson (11-6) allowed four runs on nine hits in five innings, walking two and striking out six.
He has received poor run support for most of the year.
"It was nice to see Edwin get one," Detroit manager Jim Leyland. "He's been so good for us this year. He wasn't really sharp tonight and didn't have real good stuff, except for the fourth [when he retired the side in order]."
Jackson wanted to do better with the unusual run support.
"Just enough to get a win," he said. "I'm disappointed. You want to go deep into the game when they get runs for you like that."
"All we're trying to do is get big outs at the right time and get where we want to be," Seay said.
Andy Marte homered for Cleveland.
Carlos Carrasco (0-1), making his major league debut, gave up six runs on nine hits in three innings, walking three and striking out three.
"My biggest problem was my fastball. It was all over the place," he said. "My other pitches were working, the slider and the change, just not the fastball."
Carrasco, who was obtained from Philadelphia in the Cliff Lee deal, allowed all three home runs after being recalled from Triple-A Columbus.
"He probably had the first-time jitters and we thought three innings were enough," Indians manager Eric Wedge said. "He did work hard to get through those three."
But Detroit bounced back with four in its half. Polanco and Guillen -- who has three home runs in the last two games -- each hit his ninth homer on back-to-back pitches, Huff singled in a run and Gerald Laird had a two-out RBI double.
"We just kind of caught him by surprise and got real aggressive with him," Leyland said.
Inge's two-run homer in the third made it 6-1. Huff's two-out, two-run double in the fourth made it 8-1.
"I've been here a couple of weeks. It's nice to be able to contribute," Huff said.
The Indians got three in the fifth to pull to 8-4. Grady Sizemore doubled in two and the other run scored when Guillen was charged with an error in left after catching Choo's short fly. He dropped it as he began to throw, which allowed Sizemore -- who was heading back to third -- to score.
Marte's leadoff homer in the sixth off of Zach Miner made it 8-5. It was Marte's fourth home run.
Detroit recalled RHP Jeremy Bonderman from his injury rehab assignment (shoulder soreness after surgery) at Triple-A Toledo and activated him from the disabled list. Bonderman, who had been on the 15-day DL, was 0-3 with a 5.79 ERA in 11 relief appearances in Toledo. ... The Tigers also recalled RHP Eddie Bonine, RHP Casey Fien, C Dusty Ryan, OF Wilkin Ramirez from the Mud Hens and purchased the contract of SS Brent Dlugach from Toledo. ... Cleveland purchased the contracts of OF Michael Brantley and RHP Jose Veras from Triple-A Columbus. Brantley was also in the string lineup in LF and batting ninth. He singled in his second at bat, in the fifth, for his first career hit. ... Leyland wasn't sad to see Jim Thome traded from the White Sox to the Dodgers. "I paid for his flight out there," Leyland said. Thome has 60 career home runs against Detroit.