Galvis, claimed off waivers from Toronto on August 12, followed Josh VanMeter's second hit of the game with an opposite-field drive to left. It was his second home run in two nights and career-high 21st of the season.
Aquino went 1 for 4 and his streak of consecutive plate appearances without a home run increased to 13, the longest of his brief career.
Sonny Gray struck out 10 batters in six innings, reaching double figures for the third time this season and seventh in his career. He won his third consecutive start and improved to 4-0 in his last five outings. Gray (9-6) gave up four hits and three walks.
Robert Stephenson pitched a perfect seventh inning. Amir Garrett, in his first appearance after serving an eight-game suspension for precipitating a brawl with Pittsburgh on July 30, walked the two batters he faced on nine pitches and was charged with an unearned run on Jose Iglesias's throwing error before Michael Lorenzen prevented further damage.
Raisel Iglesias pitched the ninth for his 24th save.
Cal Quantrill (6-4) almost matched Gray strikeout-for-strikeout. He tied a career-high with nine strikeouts with no walks in six innings, allowing five hits and three runs.
VanMeter led off the bottom of the first with a single to right field. He stole second and went to third on a throwing error by catcher Austin Hedges before scoring on Aquino's bloop single to right field.
Naylor tied it with his seventh homer, a two-out shot to center in the sixth. The Padres loaded the bases in the inning, but Manuel Margot lined out to center fielder Nick Senzel, ending the threat.
TRAINER'S ROOM
Padres: RHP Jacob Nix (elbow strain) allowed three hits and one walk with six strikeouts over five scoreless innings in the first start of his rehab assignment with Triple-A El Paso on Monday.
Reds: 2B Jose Iglesias was shaken up when he was smacked in the face by SS Jose Iglesias while they were chasing a pop in short center field. Both players went down and several divots were kicked up, but Galvis stayed in the game after being looked at by a trainer.
UP NEXT
Padres: No starter for Wednesday's series finale was announced.
Reds: RHP Luis Castillo set single-game career highs by allowing nine hits, eight runs and three home runs in his last start on Friday against St. Louis.
