Garza served up a career-high nine runs over five-plus innings and took the loss. In his 19 previous starts at home, dating to June 27, 2011, he had given up just three or fewer runs in each game.
With the win, the Reds now have won 11 straight games at Wrigley Field, a record for most consecutive wins by an opponent.
"For some reason, we do like playing here in Chicago," Frazier said. "Like we're happy-go-lucky here. It's pretty fun. It gets us back on that winning track. We've got two more to go, and we're trying to get that sweep for sure."
This was Garza's second start against the Reds this season. On May 26, he was upset about a pitch from Cueto that sailed over the head of David DeJesus, and after the game, Garza suggested Cueto needed to "grow up." After Tuesday's game, Garza dismissed any extra incentive.
"It's just another game," Garza said. "I know everybody made a big deal out of the whole 'Cueto vs. me' thing, but it was over the day I left [Cincinnati]. Today, I wanted to go out there and try to do the best I can and give my team a chance to win, and definitely that didn't happen. I'm just going to get out there and get ready in five days."
The Cubs were keeping an eye on Garza, who made his fifth start since coming off the disabled list. He'd lasted 6 1/3 innings in his last outing against the Angels.
"With him, it's all about fastball command and keeping the ball down," Cubs manager Dale Sveum said. "When he does that, he can throw a really good game. Every pitcher, it's going to be about his fastball command, and what happens with that will dictate the game."
Tuesday was no different.
"I don't think he really had his slider today -- he didn't throw it much," Sveum said. "It's still keeping the ball down, and keeping the ball down and away and obviously pitching in. We have to have fastball command down in the strike zone."
Frazier hit his seventh home run with two outs in the second and Votto belted his 11th with two outs in the third to open a 3-0 lead. Alfonso Soriano hit a sacrifice fly in the Cubs' fourth, but the Reds padded their lead, sending 10 batters to the plate in a six-run sixth.
Votto singled to lead off the inning and reached third on the play as right fielder Scott Hairston overran the ball for an error, one of four by the Cubs in the game. Brandon Phillips walked, and both he and Votto scored on Jay Bruce's double. Garza hit Frazier with a pitch, and Paul followed with his home run. Garza then walked Ryan Hanigan and was lifted. It's the first time he's given up three home runs in a game since last July 5 against the Braves.
"The one to Frazier was not a good pitch," Sveum said. "Votto, that was blacked out at 94-[mph] fastball, inside corner. That's the kind of hitter Votto is, he hit it opposite field into the basket. Paul, at that time, I think [Garza] was getting frustrated and just made a bad pitch."
This was one of those "tip your cap" kind of nights.
"It was impressive the way they did it," Garza said of the Reds. "Frazier hits a ball one-handed out of the yard, opposite field. Votto, inside-out with a pitch on the black. He hits it out of the yard. It's just the way it fell tonight.
"Paul yanks a fastball down and in, and it lands right on the outside part of the chalk line [in the second], then Jay Bruce inside-outs a ball and it lands on the left-field outside chalk line [in the sixth]," Garza said. "It's one of those nights -- you just brush it off and get ready for the next five [days]."
The only pitch that really bothered Garza was a hanging slider to Paul in the sixth, which ended up in the seats.
"He made me pay for it," Garza said. "That's what good teams do. They take advantage of mistakes."
Maybe the problem is Garza simply hasn't pitched enough this season.
"He's an aggressive guy, but it gets in his way a lot," Sveum said of the right-hander, who missed all of Spring Training because of a strained lat suffered before they'd even played an intrasquad game. "A lot of power pitchers, starting pitchers with that kind of stuff and secondary stuff, they've all kept the ball down as far as [Curt] Schilling and [John] Smoltz and guys with power arms who have command.
"He's got to get in that rhythm again," Sveum said. "Sometimes I talk about [Jeff] Samardzija 'Gorilla pitching,' and that's what [Garza] gets into sometimes."
Third baseman Cody Ransom, who made another error in the sixth, hit a solo home run in the Cubs sixth off winning pitcher Tony Cingrani. It was too little too late.
Zack Cozart added a three-run homer in the eighth off Zach Putnam, who then left with an elbow injury. Putnam has had problems with bone spurs and was to undergo an MRI on Wednesday.
For Garza, it's back to work. He might have been out of whack because he hasn't found a good groove with catcher Welington Castillo yet. That's what Spring Training is for.
"Being in this game for as many seasons as I have, I need to take control and I need to guide him through it," Garza said. "I'm not doing what I'm supposed to do. I'm going to get ready in five days and try to make it right."