The Mets remain 2½ games behind Appalachian League West Division leader Greeneville after the Astros lost on Sunday, but both Johnson City and Elizabethton won and are just 1½ games back from Kingsport for the second playoff spot.
Royals hurlers Sam Lewis (3-4) and Jake Newberry combined for the shutout with Lewis going six innings and Newberry tossing three to earn his first save.
Burlington (26-30) jumped out to a three-run lead in the top of the first inning on RBIs by Bobby Fisher-Brown, Pedro Gonzalez and Nick Cuckovich. Alfredo Escalera-Maldonado and Fisher-Brown added a sacrifice flies in the fourth and eighth, respectively.
The K-Mets (31-25) outhit the Royals 8-6 but stranded seven on base. Yeixon Ruiz and Jeyckol De Leon each went 2-for-4. Amed Rosario added a triple.
Kingsport starter Andrew Massie (1-2) lasted just two-thirds of an inning.
The second game of the series is Monday at 7 o’clock.