The telenovela star turned vallenato revivalist performed the song while dancers in traditional Colombian "pollera colora" dresses waved their skirts to the delight of the audience at the 14th annual awards show Thursday night.
Vives dedicated the award "to all the children of Latin America because they have made this song even bigger. And of course, to my country, Colombia."
He also racked up awards for best tropical fusion album and best tropical song by the midpoint of the show.
When Sergio George, a salsa producer from New York, won best salsa album for "Salsa Giant," and brought his fellow nominees on to the stage with him for an impromptu chorus, the public went wild and clapped along to the clave beat.
George also won for producer of the year and for best salsa song with Vives for "Volvi a Nacer."
The audience also screamed for superstar Marc Anthony and the Mexican acts: Banda el Recodito and Paquita la del Barrio's tongue-in-cheek serenade of Don Francisco from "Sabado Gigante."
Guatemalan-American singer-songwriter Gaby Moreno won best new artist.
"What an honor, my first Grammy!" she said in Spanish. "This award I want to dedicate it to all my people in Guatemala. For Guate!"
Moreno's first two bluesy albums featured both English and Spanish songs, but her third, "Postales," is entirely in Spanish.
Pitbull's "Echa Pa'lla (Manos Pa'rriba)" won for best urban performance.
"This is for all the Latinos in all the world," he said, brandishing his golden gramophone statuette.
The Argentine funk-rock duo Illya Kuryaki and the Valderramas won best urban song for "Ula Ula," while Mala Rodriguez's "Bruja" won best urban album.
Last year's big winner, the Mexican duo Jesse & Joy, sang "Llorar" with Camila's Mario Domm.
The show also paired Ricky Martin and fellow Menudo alumnus, Draco Rosa, who is touring again after being cleared of cancer earlier this year.
Two new acts, Colombia's Maluma and Inglewood, California's Becky G also paired up.
Singer/songwriter Pablo Alboran, who is massively popular in his native Spain, but not as well-known in the United States, also performed.
The show, which aired on Univision in the United States, was hosted by Mexican actress and singer Lucero.