In 1890, the Bridegrooms moved to the National League. Burns, then 26, led the league in home runs (13) and RBIs (128). He hit for the cycle on August 1, 1890. He was the first Bridegroom to do so. The Bridegrooms won the National League pennant. In the 1890 World Series, the team played against the Louisville Colonels. The series ended in a 3–3–1 tie because of bad weather. In 1892, the Bridegrooms changed their name to the Grooms. Burns's RBI total was third highest in the league. His hits, doubles, triples, and batting average were the second highest on the Brooklyn team. In 1893, between games of a doubleheader, a teammate of Burns, Tom Daly, was sleeping in center field. Burns stabbed Daly with a knife. Daly woke up and turned into the knife. This led to a severed tendon which kept Daly out for two weeks. Burns' 1894 batting average (.355) was the highest of his career. He continued to play for the club until 1895, when he left the Grooms to play for the New York Giants. In his final MLB year, Burns batted .258 over 53 games.