The No. 25 Wildcats (2-1) collected 20 hits on the day. Marcus Carson, Kole Cottam and Dorian Hairston also hit homers for UK, which had its biggest power output since the 2012 season.
Pompey went 4-for-5 to lead the Cats at the plate. The Canadian Junior National Team member drove in four runs and finished just a single shy of hitting for a cycle.
Shelby, who is off to a blazing 8-for-12 start to his junior season, had three hits and two RBI.
Starter Kyle Cody (1-0) hardly needed the strong run support. The senior right-hander worked seven shutout innings, allowing only three hits and one walk. He struck out eight and retired 20 of the last 22 batters he faced.
Sean Hjelle, Brad Schaenzer and Josh Smith closed the game out in the eighth and ninth innings.
Dayton starter Zach Beaver (0-2) suffered the loss, allowing 10 hits and three runs over five innings. The Flyers dropped to 0-3 on the season.
Kentucky returns to action on Friday with the opener of the Tony Gwynn Classic in San Diego, facing UC Santa Barbara.