Rodriguez (6-1) faced three batters over the minimum, allowing one run with four strikeouts and a walk. Both hits off him came in the second inning.
The 26-year-old righty has a 2.25 ERA, lowest among NL rookies.
Nick Hundley and Joe Panik each drove in two runs for the Giant and Gorkys Hernandez scored twice.
Starling Marte had a two-run double for the Pirates.
The Giants went 2-4 on their six-game homestand largely because their bullpen failed to hold two late leads against Houston, including one that cost Rodriguez a chance to win.
It nearly happened again.
Will Smith pitched the ninth for his eighth save.
Hundley hit an RBI triple off Joe Musgrove (4-7) in the third and singled home a run in the fourth.
Musgrove (4-7) allowed four runs on seven hits in six innings. He struck out six and walked one.
Pittsburgh utility player Christopher Bostick was acquired by Miami for cash. Bostick, who played in two games for the Pirates this season, was designated for assignment last week.
Pirates: C Francisco Cervelli did not start after getting hit in the facemask by a foul tip in the first inning of Saturday’s game. Cervelli struck out looking as a pinch-hitter in the ninth.
Giants: RHP Hunter Strickland (fractured right hand) began a rehab assignment with Triple-A Sacramento. The reliever is eligible to come off the disabled list Aug. 18.
Pirates: RHP Jameson Taillon (9-8, 3.63 ERA) faces the Twins in Minnesota on Tuesday. Taillon is 5-1 in his previous seven road starts.
Giants: LHP Madison Bumgarner (4-4, 2.69) opposes Clayton Kershaw and the Dodgers in the opener of a three-game series in Los Angeles on Monday. Bumgarner pitched seven scoreless innings against Houston in his most recent start.
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