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GLENDALE, Ariz. -- Zack Greinke felt right at home in his new uniform.

The right-hander pitched two clean innings in his Dodgers debut and Los Angeles tied the Chicago White Sox 2-2 on Sunday in a Cactus League game that was called after nine innings.

Pitching for the first time since he signed a $147 million, six-year contract to join the free-spending Dodgers in the offseason, Greinke retired six of his seven batters. He struck out leadoff man Dewayne Wise and third-place hitter Alex Rios in the first inning.

Greinke gave up one hit, a single up the middle by Jeff Keppinger.

"He knows exactly what he wants to do," Dodgers manager Don Mattingly said. "Knowing it's his first time on the mound with the umpire and everything, obviously there were no issues."

Nothing about pitching in a game in late February made Greinke feel nervous, even if it was his first with his new team. Expectations will be high with that huge contract.

"That will mostly be when the season starts," Greinke said. "Spring training is just getting ready. I kind of feel like we just got to spring training, so I didn't expect much out of it today."

Hanley Ramirez had an RBI single and Luis Cruz homered for the Dodgers.

White Sox slugger Adam Dunn hit an opposite-field, two-run homer to left against Peter Moylan. Chicago manager Robin Ventura was happy to see Dunn get his first long ball out of the way after he hit 41 last season.

"If it lingers on too much, not having good at-bats, you are starting off battling from the negative," Ventura said. "It's nice for everybody to kind of get on the board and have a good at-bat."

For his first time out, Greinke was fairly pleased to get on board with two scoreless innings.

"Maybe 50 percent of the pitches were good. That's probably more than I expected," Greinke said. "I threw one slider (to Rios) that was good. I guess that was the best pitch. Some fastballs were good, some didn't come out right. The changeups, some were lower than I wanted. The curveball was all right. It was the first start."

Greinke has been getting a franchise history lesson while hanging around Dodgers great Sandy Koufax, who attended the game.

"I just talked to him a little about baseball," Greinke said. "He's a pretty happy guy, it seems like.

"A lot of (the conversation) was just learning about how stuff was when he played, talking about stadiums and his approach to stuff."

Told that Koufax pitched 27 complete games in each of his last two seasons, 1965 and `66, Greinke was somewhat in awe.

"I don't think you could get all those guys out nowadays," he said. "You'd get tired and guys would start crushing you. I don't know if anyone is good enough to do that."

With left-hander Clayton Kershaw and Greinke on their staff, the Dodgers have the first righty-lefty combination of Cy Young Award winners on the same team since Koufax and Don Drysdale.

"I guess that's kind of neat," said Greinke, who won the award with Kansas City in 2009. "Hopefully we do that together. Those two did it with the same team so I guess that's a little more special."

Game notes

Hyun-Jin Ryu also made his debut for the Dodgers, pitching a scoreless inning before going to the bullpen for more work. Ryu was signed to a $36 million, six-year deal after the Dodgers paid Ryu's Korean league team $25.7 million for his negotiating rights. "Ryu threw a couple really good changeups and his fastball got on some guys," Mattingly said. "He looked pretty good." ... RHP Erik Johnson, rated by Baseball America as the No. 4 prospect in the White Sox system, started and allowed one run over three innings. Unlike the Dodgers, the White Sox aren't using their projected starting pitchers in games until March 1.