PHOENIX -- The Chicago Cubs ganged up on Arizona right-hander Zack Greinke in the first inning, and it was just enough to get them through.

Anthony Rizzo, Kris Bryant and Miguel Montero had one RBI apiece and four of the first five Cubs reached base in their 4-2 victory over the Diamondbacks at Chase Field on Saturday.

"We didn't want to let him settle in," Rizzo said. "We were going to try to be aggressive right out of the shoot and did a good job of getting those runs early. He ended up settling (in) against us and doing what he does to everyone, but those runs were huge for us."

Ben Zobrist had three hits and an RBI and Kyle Hendricks (1-0) gave up two runs while pitching into the seventh inning.

Zobrist singled and scored in the first inning and doubled in a run in the fourth off Greinke (0-2), who has lost the first two starts of a season for the first time in his career.

Bryant had two doubles and an RBI and Rizzo had an RBI single and two walks for the Cubs (4-1).

"We just feed off each other," Rizzo said. "We always say we are all up there together. When someone is hitting, we are all in the box with him. It's the way our team is. It's a good mix right now."

Heyward, Zobrist and Rizzo singled to drive in the first run in the first inning, and Bryant drove in the second run with a hustle double on a hard grounder that caromed off shortstop Nick Ahmed's glove into short center field.

Montero's sacrifice fly to the wall in left field made it 3-0.

"I made a bad pitch to Heyward, a bad pitch to Zobrist," Greinke said. "Besides that all right. You can't have bad at bats. I had two of them in a row to Heyward and Zobrist.

"Sometimes they are going to get hits. Ideally they get some hits on good pitches but you don't make the mistakes to get in trouble the first place. Then maybe it is one run at the most, maybe no runs if I didn't make those mistakes earlier on."

Dexter Fowler walked and scored on Zobrist's two-out double to the fence in center for a 4-0 lead in the fourth.

Greinke gave up four runs and seven hits in six innings. He struck out eight and walked three. Greinke has given up 11 runs in 10 innings in his first two starts after leading the majors with a 1.66 ERA in 2015.

Hendricks gave up one run on two hits in the first six innings before leaving after rookie third baseman Brandon Drury's RBI double with two outs in the seventh.

Hendricks struck out five and walked one. He led the major leagues with 17 no-decisions while going 8-7 last season.

"I heard a lot of comments that guys were really having a hard time picking his ball up," Arizona manager Chip Hale said. "Whether it was a breaking ball or sinker, just a funny spin to it, which sometimes happens."

Drury had two hits for the Diamondbacks (2-4).

Chris Owings singled, stole second, went to third on a groundout and scored on Hendricks' wild pitch for the Diamondbacks' first run in the fourth inning.

NOTES: Arizona CF A.J. Pollock (elbow) could miss the rest of the season after surgery to repair an acute fracture of a chronic nonunion in his right elbow, team orthopedist Dr. Don Sheridan said Saturday "If everything goes extremely well, it is going to be at least three months before A.J. starts baseball activities," Sheridan said. "It could be the entire season." A small metal place was inserted into his right elbow during this surgery. A 3-inch screw was inserted into his right elbow during a similar surgery in 2010. "Although this is a very complex problem, I am optimistic about his return," Dr. Sheridan said. ... Cubs C/LF Kyle Schwarber (knee) said he would change nothing about the play on which he suffered a season-ending knee injury after colliding with CF Dexter Fowler on Thursday. "There's nothing I would say or he would say we could do differently," Schwarber said. A date for surgery to repair torn ACL and LCL left knee ligaments has not yet been set. ... Arizona RHP Zack Greinke was 1-0 with a 1.34 ERA in his previous four starts after a loss. Greinke batted eighth in the lineup for the second time this season, and Arizona pitchers have hit in that spot five times in six games. ... The Cubs' loss at Arizona on Friday snapped a 12-game regular-season road winning streak, the team's longest since 1913.