The subject of trade speculation, Garza (2-1) allowed four hits and struck out eight in eight-plus innings for his first win since beating Arizona on May 31.
It was an outing that certainly could make Garza more attractive on the trade market. The rebuilding Cubs began the day 17 games out of first place in the NL Central, and Garza can become a free agent after the season.
The right-hander, however, didn't say much about the chatter surrounding his future.
''I'm looking forward to the next five days,'' Garza said. ''That day I face Milwaukee in Milwaukee and I'll be ready.''
Cubs manager Dale Sveum is well aware of all the speculation about Garza but doesn't want to lose a pitcher who has allowed one run over his past 15 innings, his best stretch since coming off the disabled list May 21.
''You don't want to give up those guys,'' Sveum said, ''but obviously it's a business and that's not my part of my business.''
Darwin Barney and Scott Hairston also homered for the Cubs, who had lost four of five.
Garza, who threw seven scoreless innings Sunday in a no-decision against the Mets, was three outs from his first complete game since Sept. 21, 2011, against Milwaukee when he went out to the mound in the ninth. But he walked Jose Altuve to begin the inning and was replaced by Kevin Gregg, who earned his 11th save in 11 tries.
''I'm a little upset I didn't finish it, but that's on me,'' Garza said. ''I walked a leadoff guy in the ninth and there's no reason to leave me in there. You've got a guy that's closing games really well now, so you just hand it over and watch.''
Rizzo, meanwhile, will be with the Cubs for a while and is a key to their rebuilding efforts.
The first baseman, who entered in a 4-for-40 slump, finished with two hits after the start was delayed by rain for 3 hours, 18 minutes. Rizzo agreed to a $41 million, seven-year contract on May 13 and has struggled since the deal, hitting .200 with one home run and 11 RBIs entering Friday.
Chris Carter broke up Garza's shutout bid with a leadoff homer in the seventh.
Barney was a triple short of the cycle for Chicago, which had scored 11 runs in its last five games. Hairston added a solo home run off Dallas Keuchel in the sixth to make it 3-0.
Barney has hit safely in nine of his last 10 games and has had at least two hits in three of those games.
''I've just been ready to hit every pitch, not assuming that the first pitch is going to be a ball or anything like that,'' Barney said. ''I'd be lying if I said I didn't learn something from watching those Cardinals hitters as well.''
Barney said the Cardinals, who beat the Cubs three out of four this week, ''have a good approach.'' That helped the Cubs beat the Astros, who had won six of eight.
It was the first interleague matchup between the teams after 705 meetings in the National League.
Keuchel (4-4) lost for the second time in three decisions, pitching six innings and giving up three runs and nine hits while striking out a career-high nine. Keuchel hadn't allowed multiple home runs in any outing, and only eight all season before giving up three Friday.
''I thought he made a couple of mistakes and they made him pay for it,'' Astros manager Bo Porter said. ''They were all solo home runs and he did a good job of keeping us in the game. Unfortunately, offensively we couldn't muster too much off of their guy.''
NOTES: The Cubs traded Triple-A infielder Brent Lillibridge to the New York Yankees for a player to be named or cash. Lillibridge had one hit in 24 at-bats before being sent down to Iowa on April 18. . Carlos Pena, who led the 2011 Cubs with 28 home runs, played the 1,458th game of his career but the first against Chicago. Facing Garza, a teammate on the 2008 AL champion Tampa Bay Rays, Pena was 0 for 3 before grounding out against Gregg to end the game. ... Astros RHP Edgar Gonzalez began a rehab assignment with Triple-A Oklahoma City. Gonzalez went on the 15-day disabled list with a right shoulder strain May 26. ... Houston 1B-OF Marc Krauss made his major league debut in the eighth and struck out swinging. ... Bud Norris (5-7, 3.64 ERA) pitches Saturday for Houston against Travis Wood (5-6, 2.74).
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