Choo, who hit six homers and drove in 25 runs in 27 September games, hit his 22nd home run of the year for Cleveland, which last won seven straight from August 17-27, 2008, when it won 10 in a row. Asdrubal Cbarera added three hits, while Trevor Crowe had two hits and two RBI in the win.
Fausto Carmona (13-14) improved to 3-0 against Chicago this season after allowing two runs, five hits and a walk while fanning seven in six frames.
"He was very consistent for us throughout the whole season. He always put us in position to win," Indians manager Manny Acta said. "He started out a little dicey, but adjusted after the second inning."
Brent Morel homered for the White Sox, who had a three-game win streak snapped. Tony Pena (5-3) was hammered for six runs and nine hits in six innings to receive the loss.
"Carmona is always going to have good stuff as long as he's healthy. He's one of the hardest guys to hit," Chicago manager Ozzie Guillen said.
Michael Brantley and Cabrera opened the game with consecutive doubles to put Cleveland ahead, and Choo followed with a two-run shot to right-center to open up an early three-run lead.
The White Sox used a two-out rally to get one back in the home half, as Mark Teahen doubled and scored on Dayan Viciedo's seeing-eye single up the middle.
Morel's leadoff homer in the second off the foul pole in left brought Chicago to within a run.
The Indians, though, loaded the bases with one out in the third, and Brantley scored on a wild pitch to increase the lead to two. Jayson Nix followed with a sacrifice fly for a 5-2 contest, and Crowe singled home Travis Hafner with a single to right before Pena could get out of the inning.
Crowe's RBI single in the seventh capped the Indians' scoring, and Alejandro De Aza's RBI single in the ninth for Chicago accounted for the final margin.
The Indians lead the season series, 9-7...Cleveland's bullpen had a 14 1/3- inning shutout streak broken on De Aza's hit...The White Sox bullpen broke the franchise record for single-season strikeouts. It now has 439 after Friday.