SAN FRANCISCO -- It doesn't take a pennant race to bring out the best in Arizona Diamondbacks right-hander Zack Greinke.

It just takes the San Francisco Giants and AT&T Park.

Greinke remained unbeaten in his career at the San Francisco waterfront, pitching six strong innings in the Diamondbacks' 4-3 victory over the Giants in the opener of a two-game series Tuesday night.

Welington Castillo capped a four-run fifth inning against Giants starter Johnny Cueto with a two-run single, helping the Diamondbacks win for the 13th time in their past 18 games at San Francisco.

"It's a good place to pitch," said Greinke, who improved to 4-0 in six career starts at AT&T. "Every time I pitch here, the fans are really into it."

Greinke, who helped pitch the Los Angeles Dodgers to National League West titles over the Giants in each of the past three seasons, aided his old mates' cause again Tuesday, helping them extend their lead atop the division over San Francisco (71-60) to two games.

The Dodgers (73-58) were rained out at Colorado on Tuesday.

Greinke became the third-winningest active pitcher at AT&T Park among Giants opponents by limiting San Francisco to two runs (one earned) on six hits in six innings. He walked two and struck out one.

The first-year Diamondback is now 9-1 lifetime against the Giants. The .900 winning percentage is the best of all pitchers who have made at least 10 starts against San Francisco.

"I know I've pitched a lot of good games against them," Greinke said, "but some of it is luck."

The Giants trailed 4-1 after Castillo's hit but got back within two against Greinke on back-to-back doubles by Hunter Pence and Joe Panik in the sixth inning.

Greinke (12-4) finished the inning before turning the ball over to the Arizona bullpen, which allowed one run and two hits in three innings.

Daniel Hudson, the Diamondbacks' fourth pitcher, hit pinch hitter Jarrett Parker with a pitch with two outs in the ninth and allowed an RBI single to Angel Pagan, getting the Giants within 4-3.

However, Hudson got Buster Posey to hit a shot right at second baseman Jean Segura to wrap up his second save of the season.

"We created some opportunities. We had chances out there that we couldn't cash in," Giants manager Bruce Bochy said. "That big hit was eluding us all night."

Cueto (14-5) allowed four runs on five hits in 4 2/3 innings. He walked four and struck out five.

Cueto took a no-hitter into the fourth inning and a two-hit shutout into the fifth before falling apart. Three walks among the eight batters he faced in the inning led to his undoing.

The uprising began with a walk to Yasmany Tomas, after which Chris Owings tripled to tie the game at 1-1. Cueto walked Greinke and surrendered an RBI single to Segura, scoring Owings to put Arizona on top.

A walk to A.J. Pollock loaded the bases with one out, and Cueto struck out Paul Goldschmidt to keep the Giants within 2-1. Castillo then dropped his two-run hit in front of Giants center fielder Denard Span, capping the four-run inning.

Cueto was pulled at the point.

"I personally thought Cueto has cruising until that inning," Diamondbacks manager Chip Hale said. "It's very difficult to get something going against him. But once we did, we kept it going."

Cueto had no explanation for the quick turnaround.

"I don't even know myself," he said. "Sometimes it just happens."

The Giants opened the scoring with an unearned run in the third. Brandon Crawford's sacrifice fly plated Span, who had reached base on an error by Segura.

Castillo and Pollock had two hits apiece for the Diamondbacks, who won for the third time in their past four games.

Pollock, who had his first hits of the season Sunday in his third game back from an elbow injury, also walked twice Tuesday and stole a base, Arizona's 39th this month, a team record.

Pagan had a double and two singles for the Giants, who lost to the Diamondbacks for just the second time in the past 11 meetings.

Pence, returning from a hamstring injury, had three hits, including a double, for San Francisco, which played its 14th consecutive error-free game.

The Giants out-hit the Diamondbacks 8-7.

NOTES: The only two active Giants opponents with more wins than RHP Zack Greinke (four) at AT&T Park are Los Angeles Dodgers LHP Clayton Kershaw (10) and Kansas City Royals RHP Ian Kennedy (five). ... Giants CF Denard Span left the game after six innings because of a stiff neck. ... Diamondbacks RHP Shelby Miller will be called up from Triple-A Reno to start the series finale Wednesday, Arizona manager Chip Hale saud. Miller went 5-1 with a 3.91 ERA in eight starts fir Reno since being demoted July 14. ... Hale said RHP Zack Godley, who gave up nine runs in two innings in a start Saturday against Cincinnati, would pitch out of the bullpen for the time being. ... Giants GM Bobby Evans confirmed before the game that his club was one of 28 represented at the Tim Tebow showcase in Los Angeles earlier in the day.