Casey Blake, Coco Crisp and Ron Belliard hit ninth-inning homers, and the Indians rallied from a five-run deficit to beat the White Sox 11-5 behind Victor Martinez's go-ahead single in the 11th.
"I think they feel the same way we did yesterday," said, Belliard, who turned 30 Thursday.
Wickman allowed four runs in the ninth Wednesday as the White Sox rallied to win 4-3. Takatsu took over in the ninth with a 5-2 lead in this one.
"I'm sick to my stomach right now, but there's nothing you can do about it," Chicago manager Ozzie Guillen said.
Chicago built a 5-0 lead by the fourth inning against starter Cliff Lee but was stymied by Rafael Betancourt, David Riske, Bob Howry, Arthur Rhodes (1-0) and Matt Miller, who combined for 7 2/3 innings of three-hit, shutout relief.
Crisp started the comeback with an RBI single in the fifth off Jose Contreras, and Belliard had a sacrifice fly in the seventh against Cliff Politte. Blake's homer leading off the ninth cut the deficit to 5-3.
"It seems like your chances are bleak when he comes in, especially with a three-run lead," Blake said.
Takatsu then gave up two-out homers on consecutive pitches to Crisp and Belliard.
"Whenever I come in against these guys, I can tell they really want to hit off me." Takatsu said through a translator.
After Takatsu walked Travis Hafner and gave up a single to Martinez, Luis Vizcaino relieved and retired Aaron Boone on a popout.
Vizcaino (0-1) gave up a two-run single to Martinez in the 11th that put Cleveland ahead 7-5. Boone had an RBI grounder, Blake hit a run-scoring single and Grady Sizemore followed with a two-run single.
"Our guys, they don't let their guard down, they keep going," Cleveland manager Eric Wedge said. "It's a tribute to them, not just to tie it, but to keep it going in extra innings, too."
A.J. Pierzynski hit his first home run for the White Sox, and Paul Konerko added a two-run single to back Contreras, who allowed one run and four hits in six innings.
Chicago's Tadahito Iguchi had three hits and a sacrifice fly for his first multi-hit game and RBI in the major leagues.
Scott Podsednik also drove in a run for the White Sox. Lee gave up five runs and eight hits in 3 1/3 innings.
Konerko's first-inning single put Chicago ahead and Pierzynski, who left San Francisco to sign with the White Sox as a free agent, made it 3-0 with a solo homer in the second.
Iguchi hit a sacrifice fly later in the inning and Podsednik's single in the fourth made it 5-0 and chased Lee.