The Reds had six steals in the first four innings, using six hits and four walks to build a 6-0 lead against Arrieta (7-5).
Cincinnati stole three in a three-run second inning and two in a three-run fourth. All six steals came at second base, with John Baker catching Arrieta.
"We knew it would be hard to score on Arrieta," Reds manager Bryan Price said. "We wanted to create some opportunities by being aggressive. We did a good job, all the way through, not just the first time through the lineup."
Dylan Axelrod (1-0) pitched five scoreless innings of two-hit ball and struck out eight.
"He had roughly 60 pitches in the first three innings," Price said. "It looked like he would only make it through three but he made an in-game adjustment and made it through five."
Axelrod was taking injured Homer Bailey's spot in the starting rotation and made his first start for the Reds since Aug. 16 in Colorado. Axelrod left that game with a lead, only to have the bullpen give it up.
A water main break in Denver caused a doubleheader that taxed the Reds' bullpen and Axelrod was sent to the minors in favor of bullpen help.
"It made sense," Axelrod said of that move. "You have to take advantage of every opportunity up here. They took some tough two-strike pitches in the first two innings. I decided to attack with my fastball. The three run lead made it easier.
Cubs rookie Jorge Soler doubled and singled in his second major league game and drove in a run. He homered and singled in his debut on Wednesday.
Hamilton set the tone right away. He drew a leadoff walk in the first and stole second on the next pitch.
Hamilton went 2 for 2 with a double and walked twice. Dee Gordon of the Dodgers began the day leading the majors with 58 steals.
Negron and Cozart each stole and scored in the second. Cozart and Frazier both stole and scored in the fourth.
Cozart had three hits, including a double, and scored three times.
"I've been feeling better the last three weeks but I haven't always gotten the results," Cozart said. "Now it's starting to show. We've been aggressive all year and not just with Billy. It makes it fun and creates opportunities when we run."
Arrieta felt he could have done a better job against the Reds' running game.
"I was bad at holding the runners. That's my fault," Arrieta said. "I wasn't giving Baker an opportunity to throw them out. That sets up the hits."
"Frazier hit two good pitches, but the pitch to Phillips was out over the plate, and so was the one to Hamilton for the double. I've got to vary my times better at holding the ball. They were aggressive on the bases and at the plate. They were able to get good reads and good jumps."
Jay Bruce struck out five times. He is the seventh Reds player to strike out five times in a game and the second to do it in nine innings. Adam Dunn also struck out five times in nine innings in 2002.
Cubs: 1B Anthony Rizzo was out of the lineup for the second straight day with tightness in his lower back. Manager Rick Renteria hopes to have him back for the upcoming series in St. Louis.
Reds: Bailey (right elbow) and 1B Joey Votto (left knee) are progressing at a slow rate. The Reds plan to call up seven to nine players on Monday when rosters expand to 40, according to manager Bryan Price.
Cubs: Kyle Hendricks (5-1) will open the four-game series in St. Louis on Friday. He had a rain-shortened, two-inning start Aug. 23 against Baltimore.
Reds: Mike Leake (10-11) will begin the opener of a three-game series in Pittsburgh on Friday. Leake is 5-0 in 11 starts against Pittsburgh since a 3-2 loss on May 5, 2012.
The Cubs started four players who were 24 or younger: Veteran Starlin Castro (24), who made his debut at 20, Javier Baez (21), Jorge Soler (22) and Arismendy Alcantara (22) were in the starting lineup. Billy Hamilton was the youngest Reds' starter at 23.