PHOENIX -- Lance Berkman is showing he still can swing the bat.
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"You always feel like you can do it," Berkman said, "but obviously it's good to prove it to everyone and also to yourself."
Skip Schumaker also hit a home run, Albert Pujols was 2 for 3 with two RBI, and Cody Rasmus and Gerald Laird each had three hits for the Cardinals, who got their first series victory this season.
Every St. Louis starter except Matt Holliday had at least one hit.
"We're not going to score 15 runs every night but we were swinging the bats like we were capable of," Berkman said. "We have the potential to have an explosive offense."
The Cardinals, who scored 15 runs for the first time since an 18-3 victory against Atlanta on Aug. 22, 2008, have won three of four.
"We won the series," said St. Louis manager Tony La Russa. "It's our first one and that's important. That's our goal."
Jake Westbrook (1-1) earned the victory, allowing five runs -- two earned -- on nine hits in 5 2/3 innings with two walks and three strikeouts.
"Pitching with a lead, especially one that big, it's not as easy as it seems," Westbrook said. "You can't throw down the middle and you can't walk guys because walking guys can lead to a big inning. You have to be aggressive but you can't go down the middle."
Arizona starter Ian Kennedy (1-1) lasted only three innings, his shortest outing as a starter in more than two years, allowing nine runs on seven hits with two walks and two hit batters.
"I was off on pretty much everything," Kennedy said. "The command, the curveball was getting over but nothing else was getting over. I was really battling against myself. It was pretty bad. This is by far the worst outing I've had in a long time."
Russell Branyan hit his first home run for the Diamondbacks, who gave up their most runs since a 17-3 loss to Milwaukee on May 8 last season.
"It is tough to be in a game like that but they kept battling," Arizona manager Kirk Gibson said. "It was a lot to make up. I've played in several games like that and you can push yourself as much as you want. It's frustrating. It's disappointing."
The Cardinals struck early against Kennedy, scoring two in the first and six more in the second when his control largely disappeared.
Laird beat out a grounder deep in the hole at short and Kennedy hit Ryan Theriot with a pitch. Rasmus doubled down the right-field line, scoring both runners to make it 4-0.
Kennedy walked Pujols and hit Holliday to load the bases ahead of Berkman, who hit his fourth home run of the season into the left-field bleachers to put St. Louis ahead 8-0.
Westbrook added his first RBI of the season in the third, looping a double down the left-field line to score Laird after the catcher had doubled to right.
Schumaker stretched the lead to 12-0 with a three-run homer, his first, just over the fence into the pool area in right-center field.
Branyan hit a two-run, opposite-field home run in the fourth to cut the lead to 12-2, but Pujols hit a two-run single and David Freese added an RBI hit in the top of the fifth against Aaron Heilman.
During the series, the Cardinals moved into fourth in the National League in runs scored.
"It's hard to make any judgments based on a week's worth of baseball," Berkman said. "You have to let things play out week after week."
Arizona added three more unearned runs in the fifth off Westbrook.
Kennedy lasted only two innings on Aug. 8, 2008, in Anaheim while pitching for the New York Yankees. ... Both dugouts were warned after Kennedy hit Holliday on the hand with a high, inside fastball. ... Westbrook has three RBI in 45 career at-bats. ... Laird was starting in place of Yadier Molina, who is hitting .152 (5 for 33) with three RBI and only two extra-base hits. ... The Diamondbacks optioned Kam Mickolio to Triple-A Reno before the game and recalled RHP Esmerling Vasquez. Mickolio allowed three runs on four hits in two-thirds of an inning on Tuesday. ... Before the game, the Cardinals placed RHP Bryan Augenstein and LHP Brian Tallet on the 15-day disabled list. Both were injured in the Cardinals' 13-8 loss to Arizona on Tuesday. Augenstein strained his right groin and Tallet fractured a bone in his right hand when he got rangled up with Stephen Drew on a play at first. St. Louis recalled RHP Fernando Salas and RHP Eduardo Sanchez from Triple-A Memphis. Sanchez made his major-league debut when he came on to pitch the eighth.