CHICAGO -- Bob Wickman was consistent: Pretty much everything he threw turned into a hit.
"He just didn't have it today," Cleveland manager Eric Wedge said. "The ball was up a little bit and a couple of good hitters got on them."
Wickman was the Indians' most reliable reliever last year in his second stint as their closer. He had saved 12 in a row stretching to last season.
"I throw strikes and today, obviously, it hurt me," Wickman said.
Carl Everett took a strike, then singled, and Konerko homered to left on a 1-0 pitch. After swinging and missing the next pitch, Dye homered to left-center to tie it.
"In that situation his job is to come after me and throw a strike, make me swing the bat," Konerko said. "I'm not trying to hit a home run. I'm just trying to get a base hit and keep the rally going."
Aaron Rowand took a ball, then doubled, and A.J. Pierzynski was intentionally walked.
Pinch-hitter Willie Harris' bunt was misplayed by Wickman for an error that loaded the bases, and Juan Uribe flied to right as Rowand tagged up and scored from third to win the game on the sacrifice fly.
Chicago had 46 comeback wins last year, including four after trailing in the ninth inning.
"We've got a group of guys just like last year," Harris said. "We're not going to roll over."
Damaso Marte (1-0) got the last two outs in the top of the ninth for the win.
"Winning a game like this where we hadn't swung real well in two days, I think it got the guys pumped up," Chicago manager Ozzie Guillen said. "I bet they can't wait for tomorrow to start."
Signed to a $7 million, one-year contract during the offseason, Millwood allowed four hits, struck out one and walked two as his fastball reached 94 mph. He was trying for his 99th career win, his first in the American League.
"Nothing was working a lot," Millwood said. "I didn't locate very well at all. It just seemed like I was able to make a pitch when I needed to, and that kind of got me through it."
Last year, he went 9-6 with a 4.85 ERA for Philadelphia, and the condition of his elbow was a concern to the Indians, who put special clauses in his contract to reduce their risk.
Freddy Garcia, acquired by Chicago from Seattle last season, gave up two runs and five hits in six innings, struck out six and walked three. He threw 109 pitches.
Cleveland went ahead in the second when Grady Sizemore singled and scored on a Ronnie Belliard double. Garcia walked Victor Martinez in the third, and he took third on Ben Broussard's double and scored on a balk.
- The announced attendance was 10,520 and the crowd looked even smaller. The teams drew 38,141 for Monday's opener.
- The White Sox are 2-0 for the first time since 1999.
- Under Guillen, the team is 24-7 at home in one-run games.
- Millwood hadn't gone six innings since July 31 last season.