Rodriguez had already put the Astros in great position to win by throwing seven solid innings, and when Lee socked one into the Crawford Boxes, it was time for Houston to begin celebrating its second consecutive win over the Cardinals, 11-6.
"That made me happy," said Rodriguez, who improved to 10-6 and tied his career high for wins.
The left-hander extended his winning streak to five games, and Lee homered for the second time in as many nights to send the Astros to within two games of the lead in the National League Central. The Astros, Cubs and Brewers are tied two games behind the first-place Cardinals.
Houston, which was without first baseman Lance Berkman (calf strain), has won 10 of 13 games and is 29-17 since May 30, making up seven games on the Cardinals in that stretch.
"That's all you can do is keep winning," Lee said. "When you win, you don't worry about what everybody else does. You win and you go home, and they're the ones that have to worry. It's late, but it's too early to worry about what you have to do. We have to keep playing, and hopefully down the road we find ourselves in a good spot."
Lee, whose three-run homer Monday was the difference in a 3-2 win, hit his second grand slam of the season and the 14th of his career, which is tied with Jason Giambi for the fourth most among active players. The homer sent the crowd of 33,140 into a frenzy, as Lee came back out of the dugout for a rare curtain call.
"We know we're capable of doing some damage," Lee said. "We won these first two games, and just because we won the series doesn't mean we lay down tomorrow. We have Roy [Oswalt] on the mound, and the way he's been pitching lately we have a really good chance to find ourselves with a sweep."
Oswalt will face St. Louis right-hander Chris Carpenter in a battle of aces Wednesday, but Rodriguez had the look of an ace Tuesday. He gave up four hits and one run in seven innings to improve to 4-0 with a 0.62 ERA in four July starts.
"I felt great today," said Rodriguez, who threw first-pitch strikes to 20 of the 26 hitters he faced. "I felt my arm was strong, and I used my fastball a lot and my breaking ball, too. I made one mistake [home run to Mark DeRosa in second that gave the Cards an early 1-0 lead]. It was 3-2 and I tried to throw my two-seamer, and the ball just went over the middle. He hit it very well."
The St. Louis lead didn't last long, as Hunter Pence's two-run homer in the bottom of the frame put the Astros in front, 2-1, and Houston chipped away at Cardinals starter Todd Wellemeyer (7-8) with a run in the third, fourth and fifth innings.
"I felt good the whole game," Wellemeyer said. "I was getting ahead of guys, keeping the ball down for the most part. But I was 0-2, 1-2 on a lot of guys and then they either slapped it into a hole or they got a hit or I left the ball up."
Michael Bourn singled with one out in the third, stole second and scored on a Miguel Tejada single, and the Astros went ahead, 4-1, in the fourth when Pence singled and scored on Chris Coste's double. Bourn manufactured a run for the Astros in the fifth by reaching on a bunt single, advancing to third on an errant pickoff throw and scoring on Tejada's second RBI single to make it 5-1.
"I'm trying to create havoc and get the attention off the hitter and bring it to me," Bourn said. "The more I can get it on me, the better for the hitter. I want them to leave something over the play for Lance, Miggy, Carlos and Hunter. Any given pitch they can hit out, if they're in the middle of the plate."
The Astros broke the game open with five runs in the seventh, highlighted by Lee's grand slam. The homer came after Cards reliever P.J. Watson intentionally walked Tejada, who went 2-for-3 with three RBIs.
"That's the strategy of the game," Lee said. "You're trying to put the guy on first base and get a double play. Miggy is the best hitter right now on the team and he's hitting .335, .340, and you have to take your chances. My average is lower than Miggy, and I could hit the ball on the ground and get the double play."
Geoff Blum hit the first pitch after Lee's slam 353 feet down the right-field line for back-to-back homers and a 10-1 Astros lead. Good thing, too, because St. Louis scored four runs off Chad Paronto and one off Wesley Wright in the eighth to get within 10-6.
But things are going so well for the Astros, giving up five runs late in a game didn't hurt them.
"We have a team that I think can compete with anybody right now," Tejada said. "We have a lot of veterans and a lot of guys who are really hungry to win, too. I think that if we play the way we can play and stay hungry to win, we'll show everyone how good we exactly are."
Brian McTaggart is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.