CINCINNATI — Matt Cain knew he was on the hitters’ turf, pitching in a ballpark that would magnify any mistake.

So, he didn’t make any.

Cain pitched a seven-hitter for his second shutout of the season, extending his recent run of dominance, and joined in a just-enough offense with a run-scoring single Tuesday night, leading the San Francisco Giants to a 3-0 victory over the Cincinnati Reds.

Cain (5-4) subdued the NL’s most prolific offense — Brandon Phillips had three of Cincinnati’s hits — while going the distance for the third time this season. He has all of the Giants’ complete games.

“When he’s on, he’s as tough as they get,” Reds manager Dusty Baker said.

He’s been on for some time now.

Lately, the right-hander has been the best part of one of the majors’ best rotations. Cain has pitched three complete games in his last five starts, allowing only three earned runs in 40 innings. He’s done an exceptional job of avoiding the big mistake — only four homers allowed all season.

Facing the NL’s leading lineup in one of the majors’ most homer-friendly ballparks, Cain was in control the whole way, handing Cincinnati only its fourth blanking of the season.

“It’s one of those things where you have confidence,” Cain said. “I was working all my pitches, really.”

Everything is working for him these days. Cain has given up only one run in his last 34 innings, making left-handers look even worse than right-handers. Lefties are only 4 for 58 against him in his last four starts.

“Aw, he’s been on a nice roll here,” Giants manager Bruce Bochy said. “In this ballpark, it’s quite an effort. He’s in a nice zone right now.”

So are the Giants, who have won 10 of their last 14 games and the first two in their series against the Reds, who lead the NL in homers.

Cain knew what he had to do.

“You try to keep the ball down and let your defense do the work, and they did a great job,” he said. “They made at least five great plays behind me.”

Juan Uribe hit his ninth homer into the upper deck for a 1-0 lead in the fourth off right-hander Sam LeCure (1-2), making his third start in the majors. Slumping Bengie Molina and Cain added run-scoring singles in the eighth off Nick Masset.

Uribe drove in four runs with two singles Monday night, setting up a 6-5 win in the series opener. His homer on Tuesday left him with a team-high 38 RBIs.

“This guy — you hate to think of where we would be without him,” Bochy said. “Some of the home runs he’s hit have been huge home runs, too. He’s really saved us with his play.”

Cain took it from there.

The Reds ran themselves out of a couple of early chances. Phillips was doubled off first base on a fly ball in the first inning. Scott Rolen was caught in a rundown when he tried to score from third on a grounder in the second inning with the infield drawn in — second baseman Freddy Sanchez fielded Laynce Nix’s grounder cleanly and unloaded his throw home quickly.

Cain walked two and struck out five, throwing 116 pitches. He also had two singles, a noteworthy night for the weak-hitting pitcher. Cain was 1 for 20 with 13 strikeouts coming into the game, but singled in the fifth and drove home a run with another single in the eighth.

Molina, in a 4-for-55 slump, also had an RBI single.

LeCure needed 101 pitches to last six innings, falling deep in the count. He knew that he’d have to be close to perfect, given the way Cain was throwing.

“I try not to focus on that, but you are aware that a run or two might be the difference in the game,” LeCure said. “Maybe that’s why I’m being so picky early in the games.”

NOTES: It was the Giants’ sixth shutout this season. … Sanchez went 0 for 3 with two walks, ending his 11-game hitting streak. … OF Mark DeRosa returned to San Francisco to get another exam on his sore left wrist. DeRosa was on a minor league rehab assignment when it began bothering him again. He’s been sidelined since May 9 by an inflamed nerve. … Reds LHP Arthur Rhodes retired the two batters he faced, extending his scoreless-innings streak to 23 1-3, longest by an NL reliever this season.