Cueto (17-7) was trying to become the majors' first 18-game winner. He hadn't lost a day game all season, going 11-0 in 13 afternoon starts. When rain fell in the fifth inning, it all came apart.
Rollins hit a change-up that Cueto left over the plate.
"The mound was getting slippery," Cueto said, with a team trainer translating. "It was slippery the pitch before (Rollins' homer). When it rains you expect that. It's not an excuse."
Cueto was more upset about giving up a two-out single to rookie pitcher Tyler Cloyd (1-1) that extended the inning and allowed Rollins to come to bat. The shortstop's 17th homer made it 3-1 and gave him 1,999 career hits.
"Every time we talk on the bench, the one out you want to get is the pitcher," Cueto said. "I just made the wrong pitch to him. One or two bad pitches was all it took. When you get two outs, you don't want to give up any runs."
John Mayberry Jr. added a solo homer off Cueto, who had allowed two in a game only one other time all season. It was only the fifth time in 28 starts that Cueto allowed as many as four runs.
"The pitcher's hit hurt more than anything," manager Dusty Baker said. "It extended the inning and allowed Jimmy Rollins to get up. Johnny got a changeup to Rollins, then he got another one up to Mayberry. That's it."
With relatives and friends in the stands, the 25-year-old Cloyd gave up four hits, including Jay Bruce's 30th homer, and struck out nine in seven innings. It was an improvement over his debut last week, when he gave up three runs in six innings of a 3-2 loss to the Mets.
Jonathan Papelbon warmed up before the ninth -- Phillies manager Charlie Manuel said he wanted to throw a little bit -- but got a day off after allowing a three-run homer to Chipper Jones a few hours earlier that sent the Braves to an 8-7 win in Atlanta.
Papelbon had pitched four of the last six days, so Manuel was determined not to use him.
Instead, right-hander Phillippe Aumont came on to start the inning and gave up Bruce's two-out, RBI single. He retired Todd Frazier on a weak grounder to end the game and get his first major league save.
The Reds returned from a 5-1 road trip that gave them control of the NL Central. The next chore was to move Cueto one win closer to 20 victories, a mark no Cincinnati pitcher has reached since Danny Jackson in 1988.
Cueto allowed only a pair of singles through the first four innings. Steven Lerud and Cloyd had two-out singles in the fifth, when the remnant of Hurricane Isaac brought a short burst of rain. Cueto walked around the infield, trying to clear the mud from his cleats between batters.
Rollins hit the first pitch into the right field stands, ending Cueto's streak of no more than two runs allowed in any of his last four starts. The grounds crew came out and spread a drying material around the mound.
Mayberry extended his hitting streak to five games with his 14th homer an inning later.
Cloyd gave up Bruce's homer in the second inning, then allowed only one other runner to reach second base. Cloyd has taken the rotation spot of Vance Worley, out for the rest of the season with an elbow injury.
Notes: The Reds will promote RH Todd Redmond and RH Pedro Villarreal from Triple-A Louisville on Tuesday. ... Manager Dusty Baker said players getting September call-ups shouldn't expect to play much right away. "Right now, these kids here are here to help us," Baker said. "It's not like last year when they were here to see what they could do. If we do clinch this thing, then I could play them some." ... Only three Phillies have reached the 2,000-hit mark -- Mike Schmidt (2,234), Richie Ashburn (2,217) and Ed Delahanty (2,207). ... Ryan Howard had a 13-pitch at-bat against Cueto in the fourth before grounding out.