The 33-year-old had been perfect this season, converting all 30 save opportunities and 35 in a row dating to Aug. 27, 2014.
"Frankie has been outstanding," Brewers manager Craig Counsell said. "He's been a rock all year and he'll continue to be a rock for us. But a good hitter, a great hitter, got him tonight."
The blown save spoiled what had been a spectacular comeback by the Brewers, who found themselves in a five-run deficit after a short and ugly start by right-hander Matt Garza.
Garza allowed six runs and 11 hits in 3 2/3 innings but appeared to be off the hook when Milwaukee's offense clawed its way back against Reds right-hander Keyvius Sampson.
He, too, lasted just 3 2/3 innings, but Cincinnati led 7-6 when right-hander Pedro Villarreal came on in the fourth. The Brewers loaded the bases against Villarreal but came up empty when he got center fielder Domingo Santana to look at strike three, ending the inning.
Third baseman Todd Frazier homered in the top of the fifth, giving Cincinnati a two-run cushion, but the Brewers answered with three in the bottom of the inning, trying the score 8-8 on second baseman Scooter Gennett's triple and taking the lead on a sacrifice fly from catcher Jonathan Lucroy.
"We did a great job coming back," Counsell said. "There were a lot of positive things that happened tonight. We had a huge two-out rally that got us three runs and got us back in the game and another real good rally to take the lead."
The bullpens took over there and traded zeros through the next three innings, leaving Rodriguez to work the ninth.
He had worked a scoreless inning Friday in a non-save situation, but before that hadn't pitched in a game since Aug. 19 at Miami.
Rodriguez opened the inning by allowing a single to right fielder Jay Bruce, then fell behind 2-0 to Votto on two fastballs.
Votto chased a third fastball to bring the count to 2-1 and Rodriguez followed with a fourth, high and away, that Votto sent to left for his 25th home run of the season.
Cincinnati added two more runs in the inning. A passed ball allowed Frazier to score, and catcher Tucker Barnhart made it a two-run game with an RBI single up the middle, bringing Rodriguez's day to an end.
Right-hander Aroldis Chapman came on for Milwaukee and worked a perfect ninth, notching his 25th save of the season. Right-hander J.J. Hoover picked up the victory, improving to 6-0 this season.
"With the struggles of August, we're in here savoring a win, a resilient win at that," Reds manager Bryan Price said. "We got the nice lead, 6-1, but we weren't able to hold it. We couldn't find anybody feeling it on the mound tonight until we got to (Jumbo) Diaz, (J.J.) Hoover (6-0) and Chapman.
"We treated it as a one-run game. Let's see if we can steal it late -- and we did."
NOTES: Reds OF Brennan Boesch missed his seventh straight game Saturday with a sore right ankle. Manager Bryan Price said the team had hoped he'd only miss three to five games, but there was still "a lot of inflammation" in Boesch's ankle. ... Brewers RHP Tyler Cravy will pitch from the bullpen when he returns to the active roster. Cravy has been on the disabled list with a right elbow impingement since Aug. 19 but began playing catch earlier this week and is expected to return to action quickly. ... The Reds have lost five straight games to the Brewers, who lead the season series 6-5. The Brewers are trying to win the season series with Cincinnati for the first time since 2006 when they were 10-6. ... Cincinnati scored two runs in the first inning Saturday, snapping a streak of 19 consecutive scoreless innings. The Reds were trying to avoid being shut out in three straight games for the first time since April 18-21, 1989.