CHICAGO -- Standing on the mound at U.S. Cellular Field with his family in the stands, Chase Anderson possessed the poise of a seasoned veteran.

Anderson wasn't fazed while making his major league debut Sunday against the Chicago White Sox. The Arizona Diamondbacks right-hander surrendered only one run on two hits in 5 1/3 innings and gave his a team a strong start they desperately needed.

With a command of his pitches that even impressed Arizona manager Kirk Gibson, Anderson was the winner as the Diamondbacks scored a 5-1 victory.

Right fielder Gerardo Parra and catcher Miguel Montero each hit a two-run homer to back Anderson's effort.

The opportunity never seemed to overwhelm Anderson, Arizona's ninth-round draft pick in 2009. He struck out six and walked one in his 74-pitch outing.

"I've always had a pretty good way of controlling my emotions my whole life," Anderson said. "It's just something I was born with, I guess.

"After I threw the first pitches, I was like, 'OK, this is the same game,' and it calmed me down right there. I just tried to attack the hitters. It was fun."

Anderson (1-0) faced the minimum through five innings with the only blemish coming on designated hitter Jose Abreu's single to lead off the second. Abreu was thrown out trying to stretch his single into a double, and Anderson retired the next 12 batters he faced. The 26-year-old didn't pitch out of the stretch once during his outing.

The Diamondbacks (15-25) won for the fourth time in five games. They also won a third consecutive series for the first time since June 1-10, 2012.

Parra hit a two-run homer in the fifth off White Sox starter Hector Noesi (0-3), and Montero added a two-run homer in the ninth against reliever Frank Francisco to give Arizona a 5-1 lead. Montero reached base five times.

Anderson allowed a one-out, solo home run to right fielder Moises Sierra in the sixth followed by a walk to catcher Tyler Flowers.

Gibson then replaced Anderson with lefty Joe Thatcher, who got out of the inning to maintain Arizona's 3-1 lead despite Chicago (19-20) having runners on second and third.

To stay loose between innings, Anderson does one pull-up right before going back on the field.

"I saw Tim Lincecum actually do that one time to keep his shoulder loose between innings," Anderson said. "I started doing it and had some success and kept doing it."

Arizona reliever Brad Ziegler pitched a perfect eighth to give him 18 consecutive scoreless appearances (17 1/3 innings) with 14 strikeouts. Ziegler's 18-game scoreless streak is the second longest in the majors this season, trailing only the 19-game run of Milwaukee Brewers closer Francisco Rodriguez, which ended Sunday.

White Sox manager Robin Ventura was not pleased with his team's performance in the loss.

"(Anderson) threw well, but it was pretty uninspired by us all the way through," Ventura said. "It started from the first play of the game and continued on and it stunk, pretty much the whole thing. Hector pitched a heck of a game to at least give us a chance. Everything else stunk."

Noesi continuously put himself in bad positions. Arizona's leadoff hitter reached base four of the first five innings against Noesi.

Chicago's defense didn't help the right-hander in the first inning. Center fielder Alejandro De Aza badly misplayed a ball, allowing leadoff hitter Parra to reach third on what was ruled a hit. Third baseman Martin Prado immediately gave Arizona a 1-0 lead on a single to right field, scoring Parra.

Noesi avoided further trouble thanks to two double plays -- both hit by Arizona second baseman Aaron Hill -- and four strikeouts. However, the baserunners finally caught up to him in the fifth. Parra hit an 0-1 fastball from Noesi for a two-run homer into Arizona's bullpen in right field to put the Diamondbacks ahead 3-0.

Noesi allowed three runs on eight hits in six innings. He struck out four and walked two batters (one intentionally) on a career-high 117 pitches.

"Changeup, slider, everything was working today," Noesi said. "Just one pitch that I missed up."

NOTES: Injuries are ravishing the White Sox's lineup. There have been a total of 129 games missed by Chicago players who made the Opening Day roster due time spent on the disabled list. ... White Sox manager Robin Ventura was back Sunday after missing Saturday night's game to attend the graduation of his daughter from Oklahoma State. ... Diamondbacks manager Kirk Gibson appreciates Major League Baseball recognizing Mother's Day. Players were wearing pink and some used pink bats to raise awareness for breast cancer. Gibson lost his sister-in-law, Lori Sklarski, to breast cancer in 2011. He wears a white wristband with the numbers 11-11 written on it in honor of her birthday. "Just looking at all moms and what they mean to virtually everybody, it's incredible," Gibson said. "They're like rocks. They're way tougher, too."