Joey Votto's three-run homer with two outs off Brad Lidge (1-0) tied it in the ninth.
Rhodes (2-2) hadn't allowed a run in his last 33 appearances, tying the major league season record. The left-hander gave up a leadoff double by Ryan Howard and walked Jayson Werth.
Ibanez then doubled - the ball bounced off Drew Stubbs' glove at the wall in center - for the first run allowed by Rhodes since April 10, starting the winning rally.
The comeback helped Philadelphia get beyond the loss of two starting infielders.
Philadelphia put third baseman Placido Polanco and second baseman Chase Utley on the disabled list before the game, a stunning setback for the defending NL champs.
The Phillies aren't sure how long they will be without half of their starting infield.
Polanco aggravated a troublesome left elbow on Friday. The Phillies sent him back to Philadelphia for tests to see if a bone spur is causing the lingering problems. Utley sprained his right thumb while sliding into second base on Monday night and returned to Philadelphia to see a specialist.
For one night, their fill-ins did fine.
Wilson Valdez started at second base for the first time this season and hit his third homer, a three-run shot off well-rested rookie Mike Leake. He also drove in a run on a fielder's choice in the 10th.
Brian Schneider had a three-run homer off Leake, who had his last turn skipped to cut down on his innings. The 22-year-old has thrown 95 1-3 innings - the most by any NL rookie - prompting the Reds to skip his turn last week.
Pitching for the first time in eight days, Leake left several pitches right down the middle. He gave up seven hits and six runs in six innings. In his last four starts, Leake is 0-2 with a 6.85 ERA.
Joe Blanton gave up three runs in 7 2-3 innings, and the Phillies turned it over to a closer who had blown only one save this season.
Lidge started the ninth and got the first two outs. He walked Brandon Phillips, then gave up a single by Orlando Cabrera and Votto's tying homer deep to center, his 17th. J.C. Romero pitched the 10th for his third save in four tries.
Phillies manager Charlie Manuel was ejected by plate umpire C.B. Bucknor for arguing a ball-and-strike call during the winning rally in the 10th.
NOTES: The Phillies called up INF Brian Bocock from Triple-A. ... Reds 3B Scott Rolen got a day off. ... Leake went 1 for 3 with a single. He's batting .379, hitting safely in eight of his 14 starts. ... Votto singled in his first at-bat, extending his streak to 37 consecutive games reaching base safely. It's the longest by a Red since Pete Rose reached in 48 straight in 1978, according to the Elias Sports Bureau.
