CHICAGO -- Rich Hill finally carried his pitching success from the minors to the majors.
Matt Murton, Michael Barrett and Jacque Jones also connected for Chicago, which has won seven of its last nine games.
Making his 10th career start, Hill (1-4) labored in 97-degree heat and allowed three runs and six hits. He had six strikeouts and walked one. He retired eight in a row between the second and fourth.
It was a long time coming for Hill, who made his first start on July 25, 2005, against San Francisco.
"It's great. You feel part of the team," he said.
Hill went 7-1 with a 1.80 ERA in 15 starts this season for Triple-A Iowa, but before Tuesday's game he was 0-6 with a 9.32 ERA in 15 career games in the majors.
He was uncertain why he couldn't be successful in the majors.
"It ran through my mind," Hill said. "You go down there and dominate in Triple-A and you say, 'What's going on here, why isn't it working.' Going over film before the game, I knew I had to have a good outing and it's human nature to have that, but to control that and take that one-pitch-at-a-time attitude, if you do that and simplify it you are going to be successful."
Cubs manager Dusty Baker never thought Hill doubted his talents.
"I think he might have been confused why he had such a distance between minor league performances and his big league performances," Baker said.
Eric Byrnes hit his 16th homer off Hill in the eighth inning for Arizona, which beat the Cubs 15-4 Monday night.
"They returned the favor," Diamondbacks manager Bob Melvin said. "We were swinging at balls almost chest high at times and popping it up."
Cesar Izturis, playing his first game for the Cubs, doubled in his first at-bat in the first inning and then scored on Ramirez's two-run homer off Arizona starter Claudio Vargas (8-8). It was Ramirez's second homer in two days and his 25th of the season.
Izturis was traded to the Cubs for four-time Cy Young Award winner Greg Maddux on Monday.
Juan Pierre's two-run double in the second gave the Cubs a 4-0 lead.
Barrett hit the first pitch of the third inning into the first row of bleachers in left. It was his 13th of the season. With two outs, John Mabry doubled off the wall in right-center and Murton followed with a two-run homer, making it 7-0.
The umpires didn't initially rule it a home run, but Baker argued and they reversed the call after a short meeting. Melvin argued the call briefly to no avail.
Diamondbacks reliever Brandon Medders gave up a double to Barrett in the fifth, and Jones drove Barrett in with his 17th homer.
Vargas was tagged for seven runs in four innings. He gave up three homers.
"He's just elevated. Fastballs, sliders, changeups, everything was elevated today," Melvin said.
Pinch-hitter Andy Green hit a two-run double in the fifth for Arizona.
Before the game, the Cubs recalled RHP Juan Mateo from Double-A West Tenn. Mateo took INF Todd Walker's spot on the roster. Walker was traded to San Diego on Monday for a minor league prospect. Mateo, a starter for West Tenn, was available out of the bullpen. ... Arizona OF Luis Gonzalez extended his hitting streak to 12 games.