The South Americans led 24-14 at the break and were in control for the majority of the match.
The result of this Vodacom Super Rugby encounter means the Vodacom Bulls are still the only team in the competition without a win this season.
The Vodacom Bulls came into the match desperate for a victory on their home turf, however, an erratic first-half display handed the advantage to the side from Buenos Aires. The visitors scored two tries in quick succession just before the halfway break to create a 10-point gap.
They scored three more tries in the second half to condemn the men from Pretoria to their fourth straight loss of the 2020 competition.
The Jaguares now travel to the east coast for next weekend's encounter with the returning Cell C Sharks in Durban, while the Vodacom Bulls host the Highlanders at Loftus Versfeld.
Vodacom Bulls 24 (14) – Tries: Marco van Staden, Warrick Gelant, Cornal Hendricks. Conversions: Morné Steyn (3). Penalty: Steyn.
Jaguares 39 (24) – Tries: Emiliano Boffelli (2), Rodrigo Bruni, Guido Petti, Matias Moroni, Santiago Socino. Conversions: Joaquin Diaz Bonilla (3). Penalty: Diaz Bonilla.