Vargas (2-0) retired the side in order only once in five innings and pitched out of a trio of jams, but the right-hander got the big outs when he needed them and left the game for a pinch-hitter after five innings, having checked the Astros on four singles and five walks.
"He was in jams -- seemed like every inning he was in some big jams," Brewers manager Ned Yost said. "The third, fourth and the fifth were bases-loaded jams, but he kept making pitches when he needed to and got out of it."
Vargas struck out Carlos Lee to end a bases-loaded threat in the third. He got Craig Biggio on a forceout to end another threat in the fourth.
The right-hander's biggest Houdini act came in the fifth, when his throwing error on what appeared to be a double-play ball off the bat of Luke Scott with one out, loaded the bases one more time. Vargas struck out rookie Hunter Pence and retired Adam Everett on a fly to center to end that scare.
Opposing hitters are are 0-for-8 with six strikeouts in bases-loaded situations against Vargas this season.
"Maybe he should just load them up," Jenkins said. "We were on egg shells out there today. My heart was beating wildly."
Vargas had trouble with his slider, but kept finding a way to get out of jams.
"Sometimes we seem to focus more on one guy in those situations," Vargas said. "You have to make the pitches to get out of the problem there. I can't do that all the time, because sometimes they're probably going to get a hit."
Carlos Villanueva followed Vargas and kept the shutout going until one out in the eighth, when pinch-hitter Mike Lamb homered with the bases empty to trim Milwaukee's lead to 3-1.
Derrick Turnbow finished the eighth and Francisco Cordero retired the side in the ninth. It was the 10th save in as many opportunities for Cordero, who is tied with Jose Valverde of Arizona for the Major League lead in saves.
"[The bullpen] did a great job; we were trying to get Villanueva through the sixth and the seventh, then we thought the way he was going, he could lessen Turnbow's workload a little bit if he could get one out or two outs [in the eighth]," Yost said. "[If] anybody got on, Turnbow was coming in. He got one big out and Turnbow only had to get two."
Tony Graffanino's single to right off Houston starter Woody Williams (0-3) scored Craig Counsell, as the Brewers took a 2-0 lead in the third. J.J. Hardy followed with a double -- a franchise-record 24th game in a row the Brewers have had at least one two-base hit -- to score Graffanino to put the Brewers ahead, 3-0.
"Those [two-out hits] are backbreakers," Graffanino said. "Those are obviously great to get, and it was the difference in the ballgame."
Jenkins put the Brewers ahead 1-0, with a one-out solo shot over the left-field fence in the second. It was the outfielder's fourth homer of the season.
"They had a ton of opportunities today and it was kind of a lucky victory for us," Jenkins said. "They had bases loaded three innings in a row, and with their offense, runs are going to come across the board. Lucky for us, our pitchers made some good pitches and got out of jams."
Cordero threw seven consecutive balls to start the ninth, but induced Lee to hit a 3-1 slider into a double play, then ended the game by getting Luke Scott to ground out to the right side.
"You throw seven pitches to get in trouble, and you got out of it with one -- just make your pitch," Cordero said. "I really felt I threw some pretty good pitches.
"I walked [Lance] Berkman; I tried not to let Carlos Lee get on base. I tried to make better pitches with Carlos Lee and I did. I'm never going to give in to anybody; they've got to beat me with my stuff.
Carlos Lee is a great hitter; he's a power hitter, too, but I said to myself, 'I'm better than anybody.' And if they're going to beat me, they're going to beat me with my best stuff, and I'm never going to give in to anybody."
Cordero didn't give in, and neither did the Brewers, who now head to Milwaukee for a 10-game homestand.
"We're playing good baseball and it's funny, because we're not doing anything outstanding," Graffanino said. "We're getting key hits but I wouldn't say our offense is rolling, and I wouldn't say our pitching is dominating, and we're actually not playing the best defense I think we're capable of playing. We've been kind of sloppy at times, so for where we're at and our record and what we've been doing, it's good.
"Once we start clicking, hopefully, we can really get on a roll."