Nolan Gorman had a solo home run for the Cardinals in the fifth inning, his seventh of the season.
Benito Santiago hit his first homer of the season with a three-run shot in the fourth that was a part of a four-run inning for the Redbirds.
The Royals took an early 2-0 lead with a Chris Hudgins home run to left field off Tommy Parsons.
Burlington stormed back into the game in the sixth with a pair of runs that tied the game at five. Colby Schultz hit a double to left field that scored Hudgins and then Montae Bradshaw hit a single that scored Schultz.
The Cards took the lead for good on a Zach Jackson bases-clearing double to center in the eighth that scored Luis Flores and Dariel Gomez.
Johnson City was able to stave off a Royals rally attempt in the bottom of the ninth with runners on first and second base by getting Hudgins to ground into a game-ending 6-4-3 double play.