The Royals tied it 5-5 in the eighth on Ryan McBroom's pinch-hit, two-run homer off Amir Garrett, but they couldn't keep their four-game winning streak going.
Votto saved the Reds from another rough ending.
''Joey came through as he has so many times in his career,'' manager David Bell said. ''That was a great at-bat for us as a team.''
With a designated runner on second base in the 10th, Josh Staumont (0-1) walked Nick Castellanos and Votto doubled off the wall in center, just over the glove of Brett Phillips.
''I imagine if you ask Brett he'll say that's a ball he'll catch nine times out of 10,'' Royals manager Mike Matheny said. ''The ball was hit pretty good though.''
Lucas Sims (1-0) gave up a walk in the 10th with a designated runner on second base but escaped the threat.
Matt Davidson and Jesse Winker hit consecutive homers off left-hander Kris Bubic in his first road start as Cincinnati pulled ahead 5-3, but Cincinnati's leaky bullpen let another lead slip away.
Luis Castillo limited the Royals' resurgent offense to three runs - one earned - in six innings. The Royals loaded the bases three times in all but managed only one run out of all those chances.
Bubic failed again to get a win in his third big league start. The 40th overall pick in the 2018 draft jumped from Single-A to the majors.
Kyle Farmer hit a two-run double in the second. Davidson had a two-run shot in the third, and Winker followed with a solo shot, the Reds' first back-to-back homers of the season. Bubic gave up five runs and seven hits in five innings.
''Honestly I thought I pitched better than what the linescore would look like,'' Bubic said.
The Royals repeatedly wasted bases-loaded chances and failed to take full advantage of three Reds errors.
''It's just a game that should have been ours,'' Matheny said.
Kansas City left the bases loaded in the second when Alex Gordon lined out. The Royals managed only one run out of a bases-loaded chance in the third, on Ryan O'Hearn's single.
The Royals loaded the bases again with one out in the seventh, but Farmer - playing shortstop - made a diving stop on O'Hearn's grounder up the middle and turned a double play to protect the 5-3 lead that slipped away two innings later.
Salvador Perez extended his hitting streak to nine games. Nicky Lopez and Maikel Franco extended theirs to seven games each.
LOT OF Ks
The Reds fanned 11, giving them 196 through the first 17 games, a major league record. The 2018 Astros held the previous mark of 191.
The Royals are 11-4 against the Reds since 2009, including 7-4 all-time at Great American Ball Park.
Right-handed pitcher Carlos Hernandez and lefty Asa Lacy were added to the 60-man roster. Hernandez pitched at three levels of the minors last year. Lacy, 21, was the fourth overall selection in this year's first-year player draft from Texas A&M.
Royals: Outfielder Franchy Cordero had surgery to repair a broken bone in his right wrist. He went on the injured list Sunday. Cordero was acquired from the Padres on July 16 and played in 11 games.
Reds: Reliever Pedro Strop went on the 10-day injured list with a groin injury. Infielder Josh VanMeter was recalled.
Royals: Brad Keller (1-0) makes his first road start of the season and first career start against the Reds.
Reds: Left-hander Wade Miley is expected to come off the injured list and make his second start. He suffered a groin injury in his Reds debut against the Cubs on July 27.
More AP baseball: https://apnews.com/MLB and https://twitter.com/AP-Sports
Copyright 2020 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.