Andrew McCutchen's three-run homer in the eighth inning off Logan Ondrusek brought the Bucs to within one run, but they were unable to complete the rally from an early five-run deficit, and the Reds held on for the 5-4 victory.
Brandon Phillips hit a solo home run off starter Brad Lincoln and his teammates piled on in the fourth, helping the first-place Reds extend their lead over the Pirates in the National League Central to three games.
Hurdle liked the resiliency his club displayed on Wednesday, but he's seen enough of Cueto, who made his second start against the Pirates in a week.
"We're playing good ball, we're battling," Hurdle said. "It's not like you lose it all when you get shut down by a good pitcher. That kid over there ... It's hard seeing him twice in a week when he's on top of his game."
Cueto (6-3) was beaten by the Pirates on May 30 at PNC Park, but on Wednesday he allowed just three runs on six hits in 7 2/3 innings to earn his 12th career victory over Pittsburgh.
"Everything started when I woke up," Cueto said. "I felt how good my day was going to be. When I get three, four runs ahead, that's when I come back and say that I have to get tough, I have to get strong and I have to keep throwing my game."
Cueto's outing overshadowed a gutsy effort by converted reliever Lincoln (3-1), who allowed five earned runs on six hits in four innings en route to his first defeat this season in 15 appearances, including two starts. He walked two and struck out five.
Phillips led off the second with his sixth home run of the season on Lincoln's first pitch. The pitch was down, but Phillips golfed it to right-center, putting the Reds ahead, 1-0.
In the fourth, Ryan Ludwick's bases-loaded double and an RBI single by Ryan Hanigan made the score 5-0.
"I got gassed," said Lincoln who threw 66 pitches. "I haven't gone that deep into a game in a long time. I struggled with my location in the fourth inning, got some pitches up into the zone."
Wednesday's game was a well-played, 2:44 affair, but it was not without controversy. When Cueto picked McCutchen off first base in the fourth inning, both Hurdle and the McCutchen argued with first-base umpire Bill Welke that Cueto should have been called for a balk. Hurdle said it's something the Pirates have seen from Cueto.
"[Cueto] does so many things well. He's also got the best balk move in the game," said Hurdle. "There's a break on his front knee, then the back knee breaks. We've seen the tape. You'd like to think somebody would see it. We'll bang the drum loud enough, hopefully he'll have to put it away for the rest of the season."
McCutchen was Cueto's fourth pickoff victim this season, the most among Reds pitchers and tied for the NL lead.
"I thought I saw a balk," McCutchen said. "As a basestealer, you're taught to look at certain parts of a pitcher's body. You slow the film down, you can clearly see what I see. The couple moves I saw weren't right in the rule books."
The Pirates insisted that the balk debate was not sour grapes. They had plenty of praise for Cueto, who held them to just three hits through seven innings. Cueto's 12 victories and 106 strikeouts against the Pirates are his most against any opponent.
After Lincoln exited, Doug Slaten and Jared Hughes combined for four scoreless innings to give the Bucs a chance to rally.
In the eighth, Neil Walker's RBI single drove home Rod Barajas with the Pirates' first run. McCutchen followed with a three-run homer, his 10th, to make the score 5-4.
McCutchen joined the Brewers' Ryan Braun and the Marlins' Hanley Ramirez as the only Major Leaguers with at least 10 home runs and 10 stolen bases.
"Cueto pitched a pretty good game, but we battled back," McCutchen said. "We didn't get the win. But at least we can say we battled back and gave a good effort."
Cincinnati closer Aroldis Chapman, who has not allowed an earned run in 24 appearances, pitched a perfect ninth inning with two strikeouts to earn his sixth save. He now has 52 K's in 29 innings.
The Reds' defense came through for them as well, with Barajas denied an extra-base hit in the fifth on a leaping grab against the wall by Chris Heisey.
"You see the reasons why the Reds are in first place," Hurdle said.