Munster were left sweating by the finish as they were held scoreless in the second half, with the Blues battling back to within three points of their play-off rivals.
Retired Scotland international Dan Parks had kicked Cardiff in front but Jones’ try and four successful kicks from Ian Keatley gave Munster a 16-3 interval lead.
Richard Mustoe’s 48th-minute touchdown laid the foundations for Cardiff’s comeback, but they fell just short in the end.
The Blues nosed ahead thanks to Parks’ fifth-minute opener, but Keatley punished Gavin Henson for going offside when kicking the hosts level from outside the 22.
Munster had the psychological advantage when a BJ Botha-inspired scrum won them a pressure-lifting penalty, and they struck for their first try in the very next phase thanks to Simon Zebo.
Then Henson darted through a midfield gap to set up winger Mustoe over in the right corner.