Matt Joyce capped the rout with a grand slam in the ninth off Reds infielder Alex Blandino, who was on the mound to help spare the bullpen.
After the slam, Cincinnati infielder Mike Freeman - just promoted from Triple-A Louisville - got the call to relieve and the next batter, pitcher Archie Bradley, mercifully stood with the bat on his shoulder until Freeman could get three called strikes.
''I think today was one of those days where everybody could kind of take a deep breath, sit back, enjoy it, have fun,'' said Phillies third baseman Alec Bohm, who had three hits.
Herrera, McCutchen and Rhys Hoskins all connected as the Phillies broke it open with a six-run sixth inning. McCutchen's second homer, a three-run shot, came in the eighth as the Phillies avenged an 11-1 pounding by Cincinnati on Monday.
Hoskins also had an RBI double in the fifth inning that extended his hitting streak to 10 games. Ronald Torreyes homered for the first time since 2017 and had an RBI double for Philadelphia.
''We got behind 2-0 and we get a couple home runs to get back in the game, and the guys never stopped,'' Phillies manager Joe Girardi said.
Nick Castellanos singled and doubled for the Reds to extend his hitting streak to 18 games, the best in the big leagues this season. His .361 average also leads the majors.
Tyler Naquin hit a two-run homer in the Reds second.
Phillies starter Aaron Nola (4-4) allowed three runs through five innings and induced double-play grounders to end the second, third and fourth. His fifth-inning strikeout of Jesse Winker was the 1,000th of his career.
Sonny Gray (1-4) gave up four runs in 4 2/3 innings for the Reds. The Phillies hammered relievers Heath Hembree and Amir Garrett in the sixth.
''A night to forget,'' Reds manager David Bell said. ''That's all we can do. In fact, we've already done that.''
Nola became the ninth pitcher in Phillies history to reach 1,000 strikeouts in his career and only the third to do so before turning 28. Nola, who turns 28 Friday, reached the milestone in 913 innings, more than 100 innings faster than the previous fastest, Cole Hamels, who did it in 1,042.2 innings.
OPEN IT UP
Great American Ball Park will be allowed to return to its full 42,319 capacity for the finale of the series on Wednesday afternoon. Fans will not be required to wear masks. COVID-19 restrictions have so far kept crowds below 12,000.
Phillies: Girardi said RF Bryce Harper (forearm) and SS Didi Gregorius (elbow) are swinging the bat, but the timing of their return is still uncertain. ... CF Roman Quinn will have surgery this week on a ruptured Achilles tendon and is expected to miss the rest of the season.
Reds: INF Max Schrock, who had to leave Monday's game with a left strained calf muscle after coming within a single of hitting for the cycle, was put on the 10-day injured list. Schrock said he felt a ''grab'' in his calf as he legged out a double in the seventh inning. He had the same injury to his right calf in spring training. The Reds brought LHP Cionel Perez up from Triple-A Louisville to take his roster spot. ... 1B Joey Votto (fractured thumb) will began a rehab assignment at Louisville on Wednesday. He could be back in the Reds lineup around the middle of the month. ... RHP Michael Feliz was put on the injured list with no reason specified.
Phillies RHP Spencer Howard (0-1) on Wednesday afternoon makes his third start since replacing Chase Anderson in the rotation. He has a 3.86 ERA in his first two starts. Vladimir Gutierrez (0-1) goes for the Reds. In his big league debut Friday, Gutierrez allowed just two hits and one run over five innings in a 1-0 loss to the Cubs.
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