Karsay pitched five shutout innings to win his 10th straight decision as the Indians halted the Texas Rangers' four-game winning streak, 8-0 Thursday night.
Karsay (10-1) allowed four hits in his second straight start after 42 relief outings. He worked out of a bases-loaded jam in the first inning, then gave up just two hits and one walk over the next four innings.
"I just don't know right now," Hargrove said. "I would love to give him another start, but I don't know if it is best for the club. He has been outstanding in both roles this season."
Karsay, on the disabled list from July 3 to July 26 with a strained rib cage muscle, lowered his ERA to 2.41 and became the first Indians pitcher to win 10 decisions in a row since Fritz Peterson in 1975.
"Now that I'm totally healthy, I like going out there every five days and would love to start again," Karsay said. "It is not in my hands. I will do whatever is best for the team."
Karsay stabilized a pitching staff that had been rocked by the Rangers for 34 runs in three nights.
"Karsay threw as good as any pitcher has against us this year," said Rafael Palmeiro, who went 0-for-3 after homering in three straight games.
Sexson's two-run double keyed a four-run third inning off Mike Morgan (12-8).
Roberto Alomar got a one-out single, went to second on a walk to Manny Ramirez and scored on a single by David Justice. After Thome walked to load the bases, Sexson lined a double into the gap in left-center for a 4-0 lead.
"The way Karsay was throwing, that pretty much put the game away," Texas manager Johnny Oates said.
Thome then was picked off third by Texas catcher Ivan Rodriguez, who has picked off eight runners this season, including four at third.
Jesse Levis later had an RBI single in the inning to make it 5-0.
Levis drove in Cleveland's first run with a second-inning groundout, and Thome had RBI singles in the fourth and sixth innings.
Morgan allowed five runs on seven hits over 2 2-3 innings, his second-shortest outing in 26 starts this season.
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