Billy Hamilton, who gives batterymen the shakes, went hitless but scored two of the runs in the Reds' 4-0 victory.
With the victory, Cincinnati chalked up its first series win of the season and sent the Pirates home with a 3-6 record on their first road trip.
From the 5:30 p.m. ET Tuesday resumption of Monday night's rain-suspended game to Wednesday's 2:57 p.m. ET final out, the Pirates and Reds played to three decisions within 21 1/2 hours at Great American Ball Park.
It marked the first time in 94 years that the Bucs officially played three games in one day. On Oct. 2, 1920, they participated in a formal tripleheader -- against the Reds.
The unstoppable Hamilton's partner on Wednesday was the irresistible Cueto, who threw a three-hitter with the icing of a career-high 12 strikeouts.
That's Cue-to! to you fans in Pittsburgh.
"I never think too much about those things," Cueto said of his loss in last October's National League Wild Card Game at PNC Park, where fans serenaded him. "That was 2013. This is 2014. That year is already over."
"I'm sure he was a lot more comfortable here than he was with 45,000 people chanting his name," noted Pirates catcher Tony Sanchez, who had been the straight man for Liriano's first-inning capers.
It was a loopy beginning for Liriano, leaving the impression that as soon as Hamilton had shown up, batting leadoff, the Pirates went to pieces, like hens in the henhouse when the fox appears.
The veteran lefty, though, blamed the arid conditions.
"It was too dry. The ball was slipping in my hands," Liriano said. "I couldn't get a feel."
Liriano walked Hamilton to begin the game. Hamilton stole second on the first pitch to Joey Votto -- which actually was to a third-base camera well, slicing right through Sanchez. Liriano continued making cricket pitches to his catcher, bouncing them every which way. One wild pitch sent Hamilton to third, another brought him home.
"Half of his first 12 pitches, the balls were just slick on him. He said he couldn't get a very good feeling for them," manager Clint Hurdle said.
Hamilton finally out of sight, back in the dugout, Liriano gathered himself and retired the next three men.
"To be able to finish the inning [that had begun so badly] with 19 pitches and only one run … I thought he did a very, very professional job," commended Hurdle. "And he had no more issues after that."
"I started sweating a little bit more," Liriano said simply, "and making more secure pitches."
In the seventh, Votto treated Liriano to another odd sensation: A two-run homer, the first the southpaw allowed to a left-handed batter as a Pirate, the prior one having come July 23, 2012 (Adam Dunn).
"I tried to go down and away, and wound up middle-in. Another mistake, and [hitting them] is what hitters get paid for," said Liriano, who showed rare on-field emotion when Votto's drive settled in the right-field seats, pounding a fist into his glove, punctuating an afternoon of frustration.
Cueto could have made good on the daily ration of one run the Reds have been giving him all season. But after treasuring a 1-0 lead since the opening inning, he welcomed the breathing room provided by Votto.
Without hostile fans chanting his name, as they did in PNC Park during last October's NL Wild Card Game, Cueto authored the 18th complete-game shutout in Great American Ball Park's 12-year history and the first since Homer Bailey's no-hitter last July 2 over the Giants
Then again, neither the fans nor the opponents were the same as on that Oct. 1 night that will forever be memorable in Pittsburgh. Cueto that time was undone by home runs from Marlon Byrd, who is in Philadelphia, and Russell Martin, who was in the dugout, taking a day off.
"I'm sure glad that night we didn't see this Cueto," said Sanchez, who watched the Bucs' 6-2 playoff victory from the dugout. "He had every pitch working. He threw me two different sliders, he had a fastball with a lot of giddy-up … and my last at-bat he threw me a splitter I had no clue he had. Well, I knew he had it, but he didn't show it to me until the end."
Everyone in the Pirates' lineup struck out at least once, with the exception of Jordy Mercer and, oddly, Liriano. Pedro Alvarez struck out twice, and Cueto picked up four Sanchez strikeouts -- two each of Gaby and Tony.
"I felt really strong the whole time and confident," Cueto said. "At the end of the game, I was really confident that every single pitch was good."