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ARLINGTON, Texas (Reuters) - Carlos Silva improved to a career-best 6-0 after pitching the Chicago Cubs to a 5-4 victory over the Texas Rangers on Sunday.

The big right-hander continued his resurgent year by allowing three runs in 5-1/3 innings as the Cubs got early runs on the board and claimed their sixth win in eight games.

Traded from the Seattle Mariners in the offseason, Silva had endured injuries and previously won just five games over the last two seasons.

"It's because they've been scoring a lot of runs," Silva told reporters, having become the first Cubs starter to begin the year with six wins and no losses since Ken Holtzman in 1967.

Chicago (21-24) scored four runs in the first inning, Derrek Lee with an RBI single and Alfonso Soriano hitting a two-run homer, the 299th of his career.

"I'm trying not to think about it," Soriano said of reaching the 300-homer milestone.

"I think about it before I get the at-bat, because I don't want to go to home plate thinking I'll hit one more. I think about it before and after. When you think about homers, it never happens."

Michael Young led Texas with a two-run homer in the third and an RBI double in the seventh where the Rangers (25-20) pulled within a run.

The home side had a chance to add more runs in the seventh, but Cubs reliever Sean Marshall recorded the final out with the bases loaded while Carlos Marmol came on in the ninth to earn his ninth save of the year.

Texas also lost to Chicago 5-4 in 10 innings on Saturday and have dropped two in a row after stringing together a five-game winning streak.

Starter C.J. Wilson allowed five runs in 5 2/3 innings to take the loss. He surrendered a two-out RBI single to Koyie Hill in the sixth inning where the Cubs established a 5-3 lead just as the Rangers were rallying.

(Reporting by Jahmal Corner in Los Angeles; Editing by Peter Rutherford and Clare Fallon)