The Reds outhit their hosts 16-5 and gave manager Dusty Baker his 1,620th win, which moved him past Ralph Houk into 16th place on the all-time Major League win total.
Cincinnati blew the game open with six runs in the sixth inning. Paul's homer with no one out highlighted the outburst.
Joey Votto stroked a two-run homer for the Reds and Tony Cingrani (3-0) cruised to the win with two runs on four hits over seven innings.
Matt Garza (1-1) took the loss for allowing nine runs on nine hits in five-plus innings.