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03/29/12 11:45 PM ET

Harrison fans seven in strong start vs. Giants

SURPRISE, Ariz. -- The Giants, on a night when both starting pitchers were sharp, scored three runs off Rangers reliever Yoshinori Tateyama in the top of the seventh and took a 6-2 victory at Surprise Stadium on Thursday.

Rangers starter Matt Harrison pitched six strong innings, allowing one run on six hits. He walked one, struck out seven over 91 pitches and lowered his Cactus League ERA to 1.69. Tateyama has now allowed eight runs in his last three innings.

"I think I have really been consistent this spring pounding the strike zone and getting ahead of hitters," Harrison said. "A lot of it comes from last year. The games I was successful were the ones that I was aggressive and went right after hitters. I brought that mentality into Spring Training and it has paid off."

Giants starter Matt Cain allowed just three hits in his seven innings of work, although two were home runs. Otherwise he walked just one and struck out six while lowering his ERA to 1.74. He also threw 91 pitches.

"I threw some good sliders today, and I threw some bad ones," Cain said. "I think I need to think about what I need to do to throw more good ones. It was kind of 50-50. I think next bullpen and the next start in San Fran or Oakland, I need to dial that in a little bit better."

Mike Napoli and Mitch Moreland led off the second inning with back-to-back home runs off Cain. Napoli's home run was his third in three days while Moreland's was his first since the opening Cactus League game against the Royals on March 4.

"The one pitch to Moreland, 3-2 [count], I thought I threw a pretty good middle-in pitch," Cain said. "I thought it was more in, and he put a good swing on it. I can't do much about that. The one to Napoli was more middle over the plate, kind of into his area where he likes to get extended and drive the ball up the middle of the field."

Gregor Blanco, bidding for a prominent role in the Giants' outfield, had two more hits and is now hitting .354 for the spring. Brandon Belt was 3-for-4 to raise his average to .407.

Rangers up next: Right-hander Yu Darvish pitches against the Rockies on Friday at Salt River Fields in Scottsdale. Mike Napoli will be behind the plate. This will be Darvish's last start in Arizona. The Rangers announced Thursday that Darvish will be their fourth starter and make his first Major League start on April 9 against the Mariners.

Giants up next: Barry Zito starts for the Giants on Friday against the Padres in Peoria. After getting knocked out in the third inning with five runs on nine hits in his last start, Zito needs to rebound and bolster the Giants' confidence in him as a member of the rotation. Closer Brian Wilson is expected to pitch in Peoria, making his first back-to-back appearances of the spring.

T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.