Veteran right-hander Jake Peavy makes what may be his final start in a Chicago uniform on Tuesday night when the White Sox visit the Cleveland Indians in the second game of a four-game set at Progressive Field.

Peavy, who's won 128 times in 296 big-league outings, has been at or near the top of various lists of rumored deals heading into Wednesday's non-waiver trade deadline.

He's been with the White Sox since 2009, when a July 31 deal sent him from San Diego in exchange for Aaron Poreda, Clayton Richard, Adam Russell and a minor- leaguer.

He won 11 games for Chicago in 2012 and has gotten victories in six of his last nine starts this year, including home wins against Atlanta and Detroit in his two most recent outings.

In 11 career outings against the Indians, Peavy is 5-3 with a 3.93 earned run average in 73 1/3 innings.

For Cleveland, lefty Scott Kazmir aims to maintain a perfect record at home in 2013.

The 29-year-old Texan is 5-0 in eight 2013 starts at Progressive Field, the last coming on July 13, when he defeated Kansas City with 6 1/3 innings of two-run ball.

Kazmir has gone 1-0 in two road starts since that win, picking up his sixth overall victory of the season - and first away from home - with a 10-1 triumph at Seattle on July 24.

He's 3-5 in 10 career starts against Chicago.

On Monday, Jason Giambi's pinch-hit leadoff homer in the bottom of the ninth sent Cleveland past Chicago, 3-2.

Batting in place of Mark Reynolds, Giambi's winner touched down beyond the wall in center. It gave the 42-year-old a major league record as the oldest player to hit a game-ending home run, replacing Hall of Famer Hank Aaron.

"Walk is just as good as a hit there to try to get that leadoff guy on," Giambi said. "I wasn't trying to do too much. I just wanted to see it and kind of hit it. I got a pitch up in the strike zone and ended up catching up to it."

Ramon Troncoso (1-3), who turned in a scoreless eighth inning, served up the deciding blast in defeat. Chris Perez (3-1) stranded a runner on second in the top of the ninth for the win.

Carlos Santana and Asdrubal Cabrera knocked in a run each for the Indians, who stretched their win streak to five games.

The Indians won seven of the first nine games with the White Sox in 2013, including four in a row from June 28-June 30.