"Houston has been a team that for years has given us problems," Phillies shortstop Jimmy Rollins said. "Doesn't matter if they're good or bad, they give us problems."
The Astros have owned the Phillies in recent years. They are the only NL team with a winning record (30-16) against Philadelphia since 2004.
Rodriguez (10-12) allowed one run and five hits, striking out six. The left-hander is 7-2 with a 1.79 ERA since June 24.
"It's hard to find a better pitcher over the last couple of months," Astros manager Brad Mills said.
The spoiler Astros got major contributions from three former Phillies -- pitchers Brett Myers and J.A. Happ and All-Star outfielder Michael Bourn -- to become the first team to sweep a four-game series in the seven-year history of Citizens Bank Park. They last did it in Philadelphia at Veterans Stadium in September 1999. The Astros also swept a four-game series from the Phillies in Houston last September.
Phillies starter Kyle Kendrick (8-7) allowed four runs and nine hits in six innings. He's 1-2 with a 6.23 ERA in his last three starts.
Philadelphia has struggled against the lesser teams in the majors, going 21-19 against clubs that are 10 games or more below .500.
The Phillies' inconsistent offense is struggling again, scoring two runs or less in seven of the last eight games.
"We say we're resilient," manager Charlie Manuel said. "We have to come out of it."
The Phillies are heading to the West Coast for the next six games, starting with a three-game series against the West-leading San Diego Padres.
Rodriguez allowed only one baserunner on a walk until Jayson Werth lined a single to left to start Philadelphia's fifth. Raul Ibanez followed with a double, but Rodriguez pitched out of the no-out jam without allowing a run.
"I had real good location and my breaking ball was very good," Rodriguez said.
The Phillies finally broke through in the fifth. Chase Utley lined an RBI double into the right-field corner to cut it to 4-1.
The Astros scored a run in each of the first four innings, getting key, two-out hits for the first two. Anderson Hernandez singled and scored on Lee's double to left in the first. Angel Sanchez singled and scored on Bourn's single to right in the second.
Lee connected with one out in the third, hitting a drive to deep left for his 18th homer and a 3-0 lead.
Sanchez led off the fourth with a double and scored when Rodriguez ripped a single off the scoreboard in right.
The speedy Bourn stole a run in the seventh. He reached on an infield single, stole second base despite getting picked off and scored from second on an infield single.
"Bourn was outstanding," Mills said. "God gave him some great legs and it's nice to see him use them."
The four-game losing streak is Philadelphia's longest at home this season. ... The Phillies had won their last eight day games. ... A crowd of 44,958 was the 107th straight sellout at Citizens Bank Park. ... The Astros are 16-7 in Philadelphia since the Phillies moved out of Veterans Stadium. It's the best record among NL teams. ... Phillies first baseman Ryan Howard is 3-for-24 with 12 strikeouts since returning from an ankle injury.