The funnyman won the top acting award trophy for his performance in Broadway show One Man, Two Guvnors, which scooped a total of three honours.
Corden told the crowd, "I am only one of 12 actors in our play. Without any of them it just wouldn't work. Being onstage with them is a joy."
Broadway romance Once was the evening's biggest success after landing four Drama Desk Awards, including the win for best musical.
The Drama Desk Awards, which celebrate shows both on and off-Broadway, also recognised Once for best orchestration, direction and lyrics at a Manhattan gala awards ceremony, co-hosted by Brooke Shields and Brian d'Arcy James.
The haul was a welcome boost for Once ahead of this month's (Jun12) Tony Awards, where it has been nominated in 11 categories.