"Zack is always a handful," Votto said. "John Axford is a very good pitcher in his own right, and then we stole one from him. I don't want to use the word surprising, but it's great whenever you can sneak out a win against those two pitchers."
The Reds won two of three against the struggling Brewers, leaving Baker with 1,500 victories as a major league manager.
"Every time you win something, it means something," Baker said. "They came and told me that I won my 1,400th here. Now my 1,500th here. Who knows? Maybe I'll win my 2,000th here. If I'm around that long."
"Drew always has a chance to score," Votto said. "He's such a good runner. He's probably one of the game's best runners."
Brewers manager Ron Roenicke said he didn't have a clear view of the play as it developed, but he wasn't happy with the result.
"I don't think a guy should be able to score from first base," Roenicke said.
Brandon Phillips then hit a bloop single, driving in Votto for a 2-0 lead.
Ryan Braun connected against Sean Marshall in the bottom of the ninth, trimming the Reds' lead to one with his 10th homer. Marshall nearly gave up another homer on a long fly ball by Corey Hart that was caught at the wall in center, then allowed a pair of two-out singles to Jonathan Lucroy and Norichika Aoki.
Baker then decided to replace Marshall with Logan Ondrusek.
"Aoki blooped one in there and at that point and time, I figured that was enough," Baker said. "You hate to take your closer out, but we needed that ballgame."
"As a manager, you've got to do what you've got to do," Baker said. "No, I had no reservations about that."
Axford (0-2) took the loss.
"I made a good pitch to Votto, but he put a better swing on it, got his hands in there and it was literally like an inch away from Rickie catching it," Axford said. "The ball after that, it was just kind of, throw the bat out there and hope you make contact and it dropped in. It's just the way baseball goes sometimes."
The ninth-inning offense came after impressive outings from Greinke and Cueto.
Greinke pitched eight dominant innings before being lifted for a pinch hitter. He gave up two hits with no walks and had a season-high 11 strikeouts -- his 15th career double-digit strikeout game.
Coming into Wednesday's game, Greinke was 13-0 in 18 starts with the Brewers at Miller Park -- making him the sixth player since 1900 to win each of his first 13 home decisions with a team. With Wednesday's loss, the Brewers are now 18-1 in home starts by Greinke.
Cueto pitched seven innings before Aroldis Chapman (3-0) came in for the eighth. Cueto gave up five hits, struck out five and walked one.
Cueto came into Wednesday's game on an early hot streak, having given up only six earned runs in six outings this year. He was coming off of a complete-game victory at Pittsburgh.
"He's probably the most underappreciated pitcher, since he's been healthy last year," Greinke said of Cueto. "His numbers are pretty insane. I don't think I've heard anyone talking about him being one of the better pitchers in the league. Maybe it's time to start that."
Cueto got out of trouble after the Brewers loaded the bases with two out in the third on a single by Nyjer Morgan, a walk to Weeks and an infield hit by Braun. Aramis Ramirez grounded out to end the inning.
After retiring the first 10 batters he faced, Greinke allowed a double to Stubbs in the fourth. Stubbs' double was the only hit for the Reds in the first six innings.
Braun was in the lineup despite aggravating a nagging Achilles injury Tuesday night. ... Both teams are off Thursday. Milwaukee LHP Randy Wolf (2-3, 6.68 ERA) faces Chicago Cubs RHP Matt Garza (2-1, 2.67) at Miller Park on Friday, while Cincinnati RHP Mike Leake (0-4, 5.97) faces Washington LHP Gio Gonzalez (3-1, 1.72) in Cincinnati on Friday. ... Wednesday's attendance was 27,090.