The struggling Bluebirds conceded three first-half goals for the second time in as many games as Mauricio Pochettino's men ended their wait for a win in stunning fashion
Within 15 minutes the away side had the lead at the Cardiff City Stadium, Adam Lallana firing in a cross that was steered in by Rodriguez at the back post, and the former Burnley man doubled his lead in almost identical fashion, latching onto Rickie Lambert's far-post cross.
After turning provider, Lambert then got on the scoresheet himself, trapping a loose ball inside the box before poking over and beyond David Marshall to give the away side a three-goal first-half lead.
Cardiff were without Gary Medel through illness, with Fraizer Campbell deputising, while Southampton boss Mauricio Pochettino introduced Luke Shaw, Maya Yoshida and Jose Fonte into his back four after a less than convincing defensive display in the 3-2 loss to Tottenham.
Rodriguez tried to set the early tempo for the visitors with a dangerous run forward but was stopped in his tracks by Kevin Theophile-Catherine.
The hosts spurned a huge opportunity to take the lead in the 11th minute when Peter Whittingham failed to convert Craig Noone's cross with the goal gaping and they were made to pay for that miss when Rodriguez struck twice in six minutes to put Southampton in the driving seat.
The first arrived after just 14 minutes. Adam Lallana sprung the offside trap before teeing up Rodriguez with a low pass, who converted with a simple finish.
Lambert then laid on the second with a pinpoint cross that fellow England international Rodriguez turned home from inside the box without breaking stride.
And Lambert got in on the act himself before the half-hour mark with a close-range finish, capitalising on Cardiff's poor defending from a short corner to take control of a loose ball, swivel, and then tuck it beyond Marshall.
Paulo Gazzaniga was called into action at the other end when Whittingham's shot deflected off Fonte, forcing the Italian into an excellent reflex save.
He almost undid that good work with a poor clearance a minute later, though, but Campbell could not make the most of his chance.
Mackay introduced Andreas Cornelius in place of Peter Odemwingie at the break and the hosts came out fighting; Campbell headed narrowly over from a corner and Cornelius' effort forced Gazzaniga into an unconvincing, scrambled save.
Rodriguez was denied his hat-trick by Theophile-Catherine's goal-line clearance in the closing 20 minutes as Cardiff's hopes faded.
And, despite a much-improved second-half display from the hosts, they are left looking nervously over their shoulders heading into Saturday's match with fellow strugglers Sunderland, giving owner Vincent Tan – the subject of protests before the match – plenty to think about.