The right-hander, who said he had trouble sleeping Saturday night, gave up four hits and walked two. His 28-pitch outing included only fastballs and changeups.
''Mentally, you've got to be able to control your emotions,'' Garza said. ''Everything was just fast and flying for me.''
Carlos Gonzalez had an RBI single and Michael McKenry a two-run double against Garza, who signed a four-year, $50 million deal in the offseason.
Despite the nerves on the mound, Garza said he's ''the most relaxed I've been in a couple years'' now that he knows where he'll be playing long-term.
''I have a history of not very good springs,'' said Garza, who made 24 starts combined for the Cubs and Rangers last season. ''I don't take pride in that, but I take pride in my work. When the bell rings, I'm ready to go.''
Hector Gomez snapped a tie with a homer in the eighth, and Lyle Overbay had two hits for the Brewers.
Rockies: Jorge De La Rosa also had trouble for Colorado.
He gave up a leadoff home run to Rickie Weeks and was lifted with two outs in the second inning. De La Rosa allowed four runs and four hits, walked two and threw a wild pitch. His wild throw to first base allowed a run to score.
Just like Garza, De La Rosa acknowledged he was ''too excited.'' Working on throwing more inside, he watched a fastball drift to the middle of the plate on Weeks' homer.
''My command was really bad today,'' De La Rosa said. ''Everything was up. There are things I have to work on.''
Rockies: Drew Stubbs started in center field and went 1 for 3 in his Colorado debut, four days removed from a brief hospital stay tied to a chronic condition.
Stubbs first suffered from inflammation of his esophagus, which causes difficulty swallowing, while in middle school. Brought on when he gets a piece of food stuck in his esophagus, he said it's flared up ''probably a thousand times over the years, but never to that severity.''
Stubbs said he couldn't eat or drink and got weak. Doctors on Wednesday inserted a scope down his throat to alleviate the symptoms.
''I could breathe fine and do everything except swallow,'' he said. ''It's frustrating, especially when you have other things you need to do.''
Such as win the starting job in center vacated when Dexter Fowler was traded to Houston.
''It's there for the taking,'' said Stubbs, who hit .233 with 10 homers and 45 RBIs for Cleveland last season. ''That's why I came here.''
Both managers said they would have challenged plays had the new replay system been in place.
Milwaukee's Ron Roenicke said he would have disputed Overbay being thrown out at the plate in the fifth. Colorado's Walt Weiss said he would have challenged Troy Tulowitzki being doubled off first base in the first.
''I think we need to start thinking about it,'' Roenicke said.
HOLE LOT OF WATER
What happens when a tarp has a couple tears in it? A muddy mess.
As the grounds crew at Salt River Fields removed the cover Sunday morning, they discovered the overnight rain had seeped through some undetected holes and flooded much of the right side of the diamond.
More than a dozen people spent most of the morning cleaning up. They set up electric fans, carted in dirt, used rakes, shovels and a motorized roller.
The infield was dry in time for the game. The visiting Brewers weren't affected because they took batting practice before traveling.