ST. LOUIS -- The St. Louis Cardinals are normally difficult outs for any big league pitcher, but when he's on his game, Zack Greinke is tough for anyone to solve.

The Arizona Diamondbacks' ace starter carved up St. Louis again Sunday, cruising through eight innings for his 10th win in his last 13 starts against the Cardinals as Arizona notched a 7-2 decision at Busch Stadium.

Greinke (5-3) entered the game with an earned run average at 5.08, but looked more like the guy who the Diamondbacks lavished $206 million on for a six-year deal in the offseason. He allowed just five hits, including a fourth inning solo homer to Brandon Moss, with a walk and seven strikeouts.

In his career, Greinke owns 11 wins over St. Louis, the most of any active pitcher.

"I feel like I've done good sometimes and they've done good sometimes," he said. "In my good games, they've hit the ball well sometimes but I've gotten some breaks. They hit some balls well but at least they were in the air when we could run them down."

Still, Greinke never allowed consecutive hits or more than two baserunners in any inning until Arizona established a 5-0 lead. His mix of fastballs, breaking balls and changeups were too much for a Cardinals team that has scored 10 runs or more in nine of their first 44 games.

Meanwhile, Arizona (21-25) drove St. Louis starter Jaime Garcia to cover after 2 1/3 innings with a barrage of singles and doubles. In his shortest start since June 5, 2012, Garcia yielded 10 hits and five runs, walking one and fanning none.

Garcia came into the day with a 2.86 ERA, but couldn't find an antidote for the Diamondbacks' righty-heavy lineup that is batting better than .300 against left-handed starters.

"No excuse, I just didn't get the job done," he said. "I just didn't have my stuff. I couldn't get the movement I wanted. A lot of those balls they hit, they put some good swings on them. I gave up a lot of balls in the air."

Garcia was pitching from the stretch for most of his stint, allowing three runs in the first. It appeared Garcia might minimize damage after inducing a double play grounder from Paul Goldschmidt that scored Jean Segura. But the Diamondbacks followed with four straight hits, including RBI singles by Yasmany Tomas and Brandon Drury.

Arizona manager Chip Hale said the ninth inning of Saturday's game, in which the Diamondbacks scored twice and loaded the bases before losing 6-2, carried over to this one.

"It gave us life," he said.

Arizona added a run in the second on Goldschmidt's RBI single off a 3-0 pitch. Greinke greeted reliever Matt Bowman with a sacrifice fly in the third that made it a five-run game.

The Diamondbacks capped their onslaught with two runs in the sixth as Michael Bourn's third single of the day scored Nick Ahmed and Goldschmidt's fielder's choice bouncer plated Jean Segura.

Drury, Ahmed and Chris Owings each collected two hits for Arizona, which upped its road record to 14-8 and captured its first series win in St. Louis since April 18-20, 2003.

Randal Grichuk finished the day's scoring with a two-out RBI double in the ninth, but it wasn't enough to keep the Cardinals (23-21) from falling to 12-13 at home and losing a season series to the Diamondbacks for the first time since 2013.

Greinke, who lowered his earned run average to 4.59 with this outing, said he's had plenty of run support from the offense this year. That includes a 12-7 win over St. Louis last month in which he yielded 11 hits and seven runs over 6 2/3 innings.

This time, Greinke was far stingier.

"I've had games where I've given the lead back," he said. "Today, I started out pitching well from the first inning. I wasn't giving up line drives off my fastball."

NOTES: St. Louis SS Jhonny Peralta (left thumb) continued his rehab assignment Saturday night at Single-A Peoria, playing third base and going 0-for-2. He will take Sunday off and play again Monday morning. ... Arizona RHP Josh Collmenter (right shoulder inflammation) was scheduled to make his fifth rehab start for Triple-A Reno on Sunday. ... Diamondbacks LHP Zac Curtis' scoreless eighth inning Saturday gives him eight outings and 6 1/3 innings without a run to start his MLB career.