PHOENIX -- Nobody has won more on the road than Cincinnati. No one has lost more at home than Arizona.
So the Reds' trip to the desert was true to form -- a three-game sweep for Cincinnati.
Brandon Phillips drove in four runs and the Reds finished off the series Wednesday night with a 10-3 rout of the Diamondbacks, who have gone from bad to worse since they fired manager Bob Melvin a week ago.
Willy Taveras singled three times, scoring twice, to extend his hitting streak to 14 games and Jerry Hairston Jr. doubled and tripled as the Reds won for the sixth time in seven games to climb a season-best six games above .500. Taveras had nine hits in the series, and Phillips had six hits and eight RBIs.
"We're a team that's very hungry, very young," Phillips said. "We're going out there and just playing Reds baseball the best way we know how. That's all we're really doing. We're just out there playing the game the right way."
The Reds (20-14) improved to 13-5 on the road, best in the majors. They had 26 runs and 38 hits in the series.
"Our guys are starting to hit and hitting's contagious," manager Dusty Baker said. "Guys are rooting for each other. When a guy's at the plate, guys are like 'Hey man, get you some.' That's what I like."
Cueto (4-1) allowed three runs and four hits in seven innings for his third consecutive victory. The 23-year-old right-hander had his fifth straight outing of at least seven innings.
"Johnny just made two mistakes," Baker said. "... Other than that, he was masterful. He was going to go further but we scored some more runs and some guys in the bullpen needed some work."
Phillips put the Reds ahead for good with a two-run triple in the third off 22-year-old Bryan Augenstein, who like Parra was called up from Double-A Mobile for his big league debut.
The Diamondbacks' Augie Ojeda ended a streak of 410 at-bats without a home run -- a span of nearly two years -- with a solo shot in the seventh inning.
Augenstein (0-1) gave up five runs and eight hits in 6 1/3 innings.
"It's a great feeling. It's every kid's dream," he said of his debut. "It's been my dream since I was little."
The Diamondbacks fell to 1-5 since A.J. Hinch replaced Melvin.
"It's disappointing obviously to have a homestand like this," Hinch said, "certainly nothing that we're happy about or proud of. With an off day, hopefully we can catch a little momentum going on the road."
Hinch said the Reds not only outhit the Diamondbacks but "played better defense, they ran the bases a little better, and stuck it to us."
Parra hit Cueto's 1-1 pitch 379 feet into the right-field seats in the first inning. He is the 100th player to homer in his first at-bat in the majors, according to the Elias Sports Bureau, and the second to do it this year. Jordan Schafer of Atlanta accomplished the feat in the season opener.
"I'm just real happy that I got a good swing and hit it far," Parra said through an interpreter, "and thank God it was a home run."
Stephen Drew, back in the Arizona lineup after more than a month on the disabled list (strained hamstring), had an RBI single to cut Cincinnati's lead to 3-2 in the sixth.
The Reds broke it open with five runs in the seventh. Hairston doubled in a run. Adam Rosales, Chris Dickerson and Ryan Hanigan followed with RBI singles. The other run scored on catcher Miguel Montero's throwing error.
Thursday is Arizona's only off day in a stretch of 40 games. ... Reds 1B Joey Votto was out of the lineup due to illness. He left Tuesday's game because of dizziness. ... Arizona is 0-6 in games started by replacements for the injured Brandon Webb. ... The Reds were 7 for 17 with runners in scoring position in the series.