Harrison homered on Cueto's first pitch of the game, but Heisey connected twice Sunday and led the Reds to a 3-2 victory.
"I was just ready to hit," Harrison said. "He's a strike-thrower. Sometimes when you face a guy you get familiar and you see some pitches out of his hand really well."
Heisey's solo home run with one out in the ninth off Jared Hughes (6-5) helped the Reds avoid getting swept at PNC Park. Heisey began the day with just five homers in 229 at-bats this year.
"We threw 137 pitches on the day and two of them cost us," Pirates manager Clint Hurdle said.
Jordy Mercer homered off Cueto (16-8) in the second for a 2-0 lead. Cueto wound up pitching eight innings and tied Dodgers ace Clayton Kershaw for the major league lead in victories.
Cueto worked around nine hits, striking out six and walking one. Aroldis Chapman struck two in a perfect ninth for his 29th save.
Liriano cruised through his first four innings, throwing an efficient 43 pitches before he ran into trouble in the fifth. Cincinnati's first hit off Liriano didn't come until Todd Frazier singled with two outs in the fourth.
Liriano threw a season-high 111 pitches over seven innings. He gave up two runs, five hits, three walks and struck out five.
"Everything was working down," Liriano said. "I was using the inside half of the plate, down-and-in and everything was down. I just made a mistake."
Pirates: RHP Charlie Morton (hip) threw a bullpen session before the game. He made a rehab start Thursday for Double-A Altoona. ... RHP Stolmy Pimentel (ankle) is nearing a return after throwing two innings for Altoona on Friday. ... 1B-3B Pedro Alvarez (foot sprain) began hitting off a tee. ... OF Travis Snider (hamstring) has not played since Wednesday and is still day-to-day.
Reds: After an off-day, Cincinnati starts a three-game set at Baltimore on Tuesday night. RHP Mat Latos (5-3, 3.15 ERA) opens for the Reds against RHP Bud Norris (11-8, 4.00).
Pirates: Pittsburgh begins a 10-game road trip Monday with a three-game series in St. Louis. RHP Gerrit Cole (7-4, 3.65) opposes Cardinals RHP Lance Lynn (14-8, 2.79) in a rematch of the matchup that the Pirates won 5-2 on Aug. 26.