PHOENIX (AP) — 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.

Gerardo Parra homered in his first major league at-bat but Arizona could muster little offense beyond that against Johnny Cueto.

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.’’

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.

Reds 10, Diamondbacks 3

Cincinnati Arizona

ab r h bi ab r h bi

Tavers cf 6 2 3 0 FLopez 2b 4 0 0 0

Burton p 0 0 0 0 Parra cf-lf 4 1 1 1

HrstnJr ss 5 3 2 1 J.Upton rf 3 1 2 0

Bruce rf 3 2 0 0 S.Drew ss 4 0 1 1

Phillips 2b 4 1 2 4 LRosls p 0 0 0 0

RHrndz 1b 4 1 1 1 Byrnes lf 3 0 0 0

ARosls 3b 4 1 1 1 JGutrrz p 0 0 0 0

Dickrsn lf 4 0 2 1 Vasquz p 0 0 0 0

Hanign c 5 0 2 1 RRorts 3b 1 0 0 0

Cueto p 4 0 1 0 Monter c 3 0 0 0

Herrer p 0 0 0 0 Tracy 1b 3 0 0 0

DMcDn ph-cf 1 0 0 0 Ojeda 3b-ss 4 1 1 1

Agnstn p 2 0 0 0

Schnws p 0 0 0 0

CYoung cf 1 0 0 0

Totals 40 10 14 9 Totals 32 3 5 3

Cincinnati 003 000 520 — 10

Arizona 100 001 100 — 3

E—R.Hernandez (2), Montero (4), Augenstein (1). DP—Cincinnati 1, Arizona 2. LOB—Cincinnati 9, Arizona 5. 2B—Hairston Jr. (6), Phillips 2 (7), J.Upton (7). 3B—Hairston Jr. (1), J.Upton (1). HR—Parra (1), Ojeda (1). SB—Taveras (10), Hairston Jr. (4), Bruce (3).

IP H R ER BB SO

Cincinnati

Cueto W,4-1 7 4 3 3 2 4

Herrera 1 1 0 0 0 2

Burton 1 0 0 0 1 1

Colorado

Augenstein L,0-1 6 1-3 8 5 5 2 3

Schoeneweis 0 0 1 1 1 0

J.Gutierrez 1-3 3 2 2 1 1

Vasquez 1 1-3 2 2 2 0 1

L.Rosales 1 1 0 0 0 1

Schoeneweis pitched to 1 batter in the 7th. HBP—by Vasquez (Bruce), by Augenstein (A.Rosales). WP—Vasquez. Umpires—Home, Rob Drake; First, Dana DeMuth; Second, Doug Eddings; Third, Hunter Wendelstedt. T—2:58. A—20,443 (48,652).