"We've be playing outstanding the last (seven) games, " Zambrano said. "We've been doing the right things, playing good defense. We've been doing the things everybody was expecting from us. That's what this team is capable of. We have a good team."
The Cubs pounded Cueto for five runs and seven hits in 3 2/3 innings and have won seven in a row for the first time since Aug. 23-29, 2008.
"When you're up against Cueto, you probably figure it's not going to be the kind of day we had," Cubs manager Mike Quade said. "(Cueto) kind of makes it tougher. (Zambrano) was great."
Cueto (7-5) hadn't allowed more than three earned runs over a span of 17 starts dating to last season but allowed season highs in hits and runs. The homer he allowed to Zambrano ended a streak of six starts without a long ball.
"(Cueto) wasn't sharp," Reds manager Dusty Baker said. "He wasn't sharp early in the count. We were hoping he would get sharp like he can sometimes. But he was spinning off and missing the outside part of the plate."
Starlin Castro drove in four runs for Chicago, his highest RBI total since he drove in six in his major league debut May 5, 2010. He doubled and singled, raising his NL-best hit total to 148.
"(Castro is) playing great," Quade said. "(I am) looking to give him a day off, but not right now."
Carlos Pena doubled twice, walked, was hit by a pitch and drove in three runs for Chicago. Aramis Ramirez reached base four times on two singles, a walk and a hit by pitch and scored twice. Pena said it was the Cubs' collective approach that allowed them to get to Cueto.
"He gets a lot of hitters to chase and we were able to lay off some pitches, get on base and get the big hit," Pena said. "It was just a good approach overall."
Alfonso Soriano also was on base four times and scored twice. He singled, doubled and drew a pair of walks. Reed Johnson singled, doubled and scored three runs. Johnson said everything is coming a little easier for the disappointing Cubs, who fell to 23 games under .500 before embarking on their current streak.
Reds second baseman Brandon Phillips had to leave the game with a sprained right ankle after colliding with center fielder Drew Stubbs in the fourth. Phillips was able to finish the inning but was removed for pinch hitter Todd Frazier in the fifth.
"That was a blessing that my foot was in the air a little bit and I had on the rubber cleats today," Phillips said. "If I had on my metal cleats today, I probably would have been done. I work on that play every day. I knew I was going to catch it, I just have to work on getting hit.
"I'm feeling all right, he added. "I was just talking to the doc, he said just to make sure I don't sit around, just make sure you walk around a little bit and keep your foot elevated."
Zambrano (9-6) overcame early control problems. He allowed six hits and four walks and struck out six. One of the top hitting pitchers, Zambrano's solo homer in the third opened the scoring for Chicago and gave him seven career homers against Cincinnati.
"It was a good pitch to hit and thank god I was able to crush it," Zambrano said.
Yonder Alonso drove in two runs and hit his first major league homer for the Reds, who have lost four of five and 11 of their past 15 on the road.
"It's nice to get that home run so it's not a '0' anymore, it's a '1' in there," Alonso said.
Cueto has baffled National League hitters recently with a revamped delivery in which he twists his body in a manner similar to former Red Sox pitcher Luis Tiant. The Cubs were seeing his new approach for the first time on Saturday but thrived anyway.
"You see that from some Japanese pitchers," Johnson said. "(Hideo) Nomo was a little bit more extreme than that. It's tough from a timing standpoint. You've got to see it a couple of times because last time we saw him, he wasn't like that."
Cueto allowed seven hits, five runs, three walks, a homer, hit two batters and threw a wild pitch in 3 2/3 innings, striking out two.
Postgame talk in the Cubs clubhouse focused on a home run for the second straight day. On Friday, speedy Tony Campana legged out an inside-the-park homer, his first major league home run. Zambrano's majestic shot on Saturday couldn't have been more different.
"I'm no Campana," Zambrano said. "I'm a big man, I'm supposed to hit the ball with authority. Inside-the-park, I'm going to leave it to Campana."
It was the 23rd career homer for Zambrano, moving him into a tie with Walter Johnson for ninth on the all-time list for home runs as a pitcher.
"Every time you win, it's fun," Pena said. "We've been winning so it's been a blast. Everything feels just a little bit lighter."
Campana wasn't in the Cubs' lineup one day after his career-best game on Friday. Quade said that he'll continue using Campana as a bench player and occasional starter for the time being. ... After wavering slightly in his pregame talk with the media on Friday, Quade said that Rodrigo Lopez will make his next start despite his poor recent outings in which he's allowed 12 runs in 8 1/3 innings. ... Chris Heisey was held out of the Reds' lineup for the third straight game because of a sore oblique muscle caused by a swing in batting practice Wednesday in Houston. The Reds said he would likely be placed on the DL Sunday. ... Zambrano has now driven in a run and earned a victory in the same game 38 times in his career, breaking a tie with Washington's Livan Hernandez for the most among active players.