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CHICAGO -- Anthony Rizzo's arrival in Chicago has generated hype throughout the city. It's also given a last-place team such as the Cubs an encouraging glimpse of the future.

Rizzo hit his first homer in a Cubs uniform Saturday, a two-run, go-ahead shot to spark a 3-2 victory over the Houston Astros. He now has two game-winning hits in four games and Chicago is 3-1 since he joined the team.

"It's good to come into a new clubhouse and produce like that and help the team win," said Rizzo, who also made a nice play in the field to cut down a run. "It's a lot of fun when you do that. It's just good to win."

Matt Garza (4-6) struggled but got the victory by working 5 1/3 innings. Five Cubs relievers combined to allow one hit and no runs over the final 3 2/3 innings with Carlos Marmol pitching the ninth for his seventh save in nine chances.

Rizzo has worked to shorten up his swing since spring training and put up impressive numbers at Triple-A. And his homer Saturday -- the second of his career after hitting one with the Padres last season -- came off a left-hander in J.A. Happ.

"That's another thing I worked on hard this year, hitting lefties and I feel comfortable if it's a lefty or righty," he said.

Said Garza: "He's doing a great job producing and doing what he does."

"Let the guy enjoy it," he said. "Let him enjoy his ride."

Happ (6-8) allowed five hits, four walks and three runs in six innings. But the former Northwestern University pitcher is winless in his past 11 road decisions dating to May 3, 2011.

"It's frustrating. It was a walk, a bloop and a blast, then a loss," Happ said. "It's tough taking that, but other than that I felt good out there."

Veteran Astros first baseman Carlos Lee, the subject of trade rumors involving the Los Angeles Dodgers, went 0 for 4. He said after the game he would talk to his wife about whether to accept the move.

"Probably tomorrow I'll let you know," Lee said after the game. "Because I don't want to go through this. Either I'm going or I'm not."

Rizzo's long and high drive to right field scored Starlin Castro for a 3-2 lead. Moments earlier, Castro had hit a two-out RBI single for Chicago's first run.

Garza labored on the 92-degree afternoon but was backed by three double plays and some overly aggressive baserunning by the Astros. He gave up two runs and nine hits in 5 1/3 innings and threw 104 pitches with three walks. Scott Maine relieved him in the sixth and gave up a single to Jason Castro, but Cubs left fielder Alfonso Soriano made a strong throw to get Chris Johnson trying to make third on the hit.

A leadoff single by J.D. Martinez, a double by Scott Moore and a single by Jordan Schafer gave the Astros a 1-0 lead in the third. But a big inning was averted when Rizzo fielded Jed Lowrie's grounder to first base and made a strong throw to the plate to easily nail Moore.

"That's my go-to place," Rizzo said. "Hitting's going to come and go but fielding's going to be the consistent thing I pride myself on all the time. That's where I go to."

Martinez hit a two-out RBI single in the fourth, right after the Cubs had turned a 5-3 double play with two runners on. But he was caught off second after initially heading for third on Moore's single and was tagged out to end the inning.

"I'm not exactly sure what J.D. was doing. C.J., I don't really mind as much, he was trying to bust his tail to get to third with one out with Soriano, who's known not to have the best arm around, and he was going to his left," Astros manager Brad Mills said. "I'm not exactly sure what happened to J.D. because he was halfway to third and he stopped."

Lowrie saved a run in the fourth with a great stop on Darwin Barney's hard two-out grounder to shortstop, shoveling it backhanded to second baseman Moore for the out.

Game notes

Astros 2B Jose Altuve (right hamstring) ran sprints on Saturday and there is a chance he could play Sunday after missing six straight games. ... Cubs 3B Ian Stewart could be headed for surgery after his injured left wrist has not responded to treatment. .... Cubs RHP Ryan Dempster (DL with a lat injury) is slated to throw a bullpen session Monday in Atlanta. ... Mills said he's hoping RHP Wilton Lopez (right elbow sprain) will be ready to return after the All-Star break. Lopez is scheduled to throw a bullpen session during the team's next stop in Pittsburgh.