Houston was held to four hits -- including two doubles by Jeff Keppinger -- as Zito fired six scoreless innings to best Rodriguez, who carried a shutout in the sixth before allowing three runs.
Considering Rodriguez struggled in the spring with a 12.10 ERA, his outing against the Giants was a relief to the Astros. The Astros' Pitcher of the Year from 2009 allowed seven hits, three runs and four walks and struck out four batters while throwing six innings.
"He came out pitching right away and his command was a lot better than it was in the spring," Mills said. "Maybe he was a little bit more attentive or whatever you want to say. It was nice to see him throw the ball extremely well and hit the corners like he was and have command of his pitches."
On Monday, it was reigning National League Cy Young winner Tim Lincecum who baffled the Astros for seven scoreless innings, which wasn't surprising or too unexpected. But Zito nearly matched him, giving up just three hits and one walk and striking out five batters.
The Astros are hitting .194 (13-for-67) through two games, including 1-for-13 with runners in scoring position. They were 0-for-6 with runners in scoring position Tuesday, wasting a pair of one-out doubles by Keppinger in the first and the sixth.
"We need to pick up the offense," said Keppinger, who started at second base against a left-hander. "We need to score runs to win. It's tough when you get shut out. We're going to have to battle and do little things to scratch runs across and play good defense. Hopefully things will turn around for us tomorrow."
Keppinger came close to hitting the Astros' first home run of the season when he lifted a fly ball to left field in the sixth that caromed off the top of the wall and back into play. Keppinger stopped at second with a double, prompting Mills to jog from the dugout to argue that it should have been a homer.
"I haven't looked at it on replay, but to me when I saw it, it looked like it bounced awful high and awful far out," Mills said. "That's why I asked them to look at it, and they weren't sure either until they looked at it."
After reviewing the replay for several minutes, the umpires emerged from the tunnel and confirmed the ruling on the field. The Astros then proceeded to strand Keppinger at second when Pence flied out to left and Carlos Lee popped out.
"We're only two games in," Mills said. "But there is some anxiety there as well, maybe trying to do too much. I don't want to start labeling guys too early. There's some things we want to look at in being ahead in the count and swinging at some questionable pitches. We'll look at it. But at the same time the anxiety level goes with the at-bats as they go a little bit deeper into the game. For the most part, we want them to stay aggressive."
Rodriguez benefitted from double plays in the second, third and fourth innings, with Keppinger turning two throws from Chris Johnson at third base and one from Tommy Manzella at shortstop. The lefty held the Giants scoreless until the sixth, an inning that began with a pair of four-pitch walks to Edgar Renteria and Pablo Sandoval, both of whom eventually scored.
"I lost my location," Rodriguez said.
Aubrey Huff shot a single to right-center to score Renteria for a 1-0 lead, and Rodriguez nearly watched another 5-4-3 double play unfold behind him, but a hustling Mark DeRosa beat the throw to first. Sandoval darted home on a sacrifice fly to right-field foul ground, just beating a swipe tag by catcher Humberto Quintero, and Juan Uribe had an RBI single on the next pitch to make it 3-0.
"Obviously, we don't have the burners on this team, but you don't have to be a speedster to be a good baserunner," said Giants first-base coach Roberto Kelly, who handles baserunning. "That showed today. Those are the things you're going to have to do to score some runs. We worked on that in Spring Training, and it's showing now, which is good."
In addition to the good defense the Astros have displayed through two games, both Roy Oswalt and Rodriguez delivered quality starts, and the bullpen has thrown the ball well. Relievers Brandon Lyon and Matt Lindstrom made their Astros debuts Tuesday and pitched scoreless innings.
Now it's up to the offense to get on track in Wednesday's series finale against the Giants' Matt Cain.
"The good thing about these first two games is how good our pitching has been," Pence said. "The bullpen, everyone's been solid. Wandy and Roy both had great starts, quality starts. We've just got to start scoring runs and swing the bats. Maybe it's a little bit of trying to do too much. Hitting is contagious. We've just got to get that first win and then maybe we can relax a little bit."