The Astros rallied for two runs in the ninth, winning on Reggie Abercrombie's RBI double.
Oswalt struck out two and was pleased his performance despite spending a lot of time behind in the count. He threw 22 strikes and 14 balls.
"The ball was coming out of my hand well," he said. "I missed a few spots early in the count, but I was able to come back and work through it."
Oswalt threw a few offspeed pitches.
"I was trying to get command of my fastball, which is my No. 1 pitch," he said. "I threw two curveballs, two sliders and two changeups. Other than that, it was fastballs."
Valverde, acquired from Arizona to be the Astros' closer, struck out two in a hitless inning. He led the majors with 47 saves last year.
"He knows how to turn it up," Astros manager Cecil Cooper said. "He's one way when he's not pitching and another way when he is pitching. He knows when to dial it up when he has to dial it up. Today, he dialed it up pretty good."
Indians starter Paul Byrd stuck with fastballs and allowed one run and four hits in two innings.
"It was nice to get the feel of the ball again, try to throw some fastballs," Byrd said. "It's good to get in some trouble and then get out of trouble."
Byrd is currently awaiting Major League Baseball's decision on his admitted use of human growth hormone.
Japanese right-hander Masahide Kobayashi pitched in his first game for the Indians. He worked himself in and out of a bases-loaded jam, striking out Victor Diaz to escape.
Through a translator, Kobayashi said his nerves helped him focus and he "just wanted to focus on getting outs one by one."
Kobayashi signed a two-year contract with the Indians after nine seasons in the Japanese Pacific League. Cleveland got him to add depth to the bullpen behind closer Joe Borowski, who retired all three batters he faced in the third inning.
"He had good action on his pitches," Cleveland manager Eric Wedge said. "It was pretty impressive the way he worked out of that jam."
"We'll probably mix Kobayashi in the sixth, seventh, eighth innings," he said. "I have confidence anywhere we put him."
Notes: New Astros 2B Kazuo Matsui was a late scratch from the starting lineup because of hemorrhoids. He is expected to play Saturday against Atlanta. ... Houston 1B Lance Berkman, who strained an oblique muscle early in spring training, will start Sunday in a split-squad game against Washington. ... Cleveland LHP C.C. Sabathia will make his spring debut Saturday against Detroit. Dontrelle Willis will start for Detroit.