Born in San Antonio, Texas, in 1943, Jesse Ponce grew up in the heart of conjunto music, a traditional accordion-led style of Tejano (or Tex-Mex) music. His first performing was done with Conjunto Ponce, a family band led by his father Encernación Ponce, a violinist and accordion player born in Monterrey, Mexico. Jesse began playing the bajo sexto (12-string guitar) at age seven, though today he is best known as an accordionist. In 1964, Ponce joined the band of conjunto superstar Flaco Jiminez and worked with him three years. The two linked up again in 1977, when Jiminez was playing with acclaimed roots musician Ry Cooder. This association led to a European tour, an appearance on Saturday Night Live and a live album.

A resident of Toledo since 1979, Ponce took up the three-row button accordion in the early 1980s since there were so few players in northwestern Ohio. He still plays bajo sexto occasionally with Amanda Reyna y los Reyes Ritmo, but he's more frequently found playing his beloved rancheras and polkas on his squeezebox. He currently performs with Baldemar Velasquez in the Aguila Negra Band, with Jacob Estrada and Frank Ibarra in Sal y Pimienta and as the "house musician" at the Sofia Quintero Art and Cultural Center in Toledo. In addition to his performing activities, Ponce has long been an active and central part of the Latino community in northwestern Ohio, mentoring young musicians, working with the Farm Labor Organizing Committee, and participating in countless benefit concerts.