Emiliano Boffelli punished error-strewn England by booting six penalties, before racing in for a well-worked try. Santiago Carreras raced in for a score of his own, with England struggling for fluency or rhythm.
Cheika will have been delighted to have put one over old friend and England boss Jones, but that will have paled into comparison alongside the magnitude of this result for the South Americans.
England will face Argentina again in the World Cup next year, with Jones admitting this clash would prove a mini dress-rehearsal for that global tournament clash in France.
The hosts fluffed the audition, too often losing their place in the script.
Joe Cokanasiga powered home for a fine score and replacement Jack van Poortvliet handed England hope with a classic scrum-half try.
Owen Farrell kept the scoreboard ticking with five penalties and two conversions, but England cannot come away from this game and say they did themselves justice.
Cokanasiga’s try and Farrell’s boot allowed England to turn around 16-12 to the good at half-time.
England stymied their own progress time and again in that first 40 however, with a string of errors at kick-offs and restarts. Yes, the pitch was sodden, yes, the ball was greasy, but no, England should not have kept fluffing their lines at the sport’s unofficial set-piece.
The Pumas were more than happy to profit from England’s untidiness, with Boffelli posting all four of his penalty opportunities.
England’s invention was limited to Ben Youngs’ cute chip that so nearly set Smith clear for a score.
The hosts built the pressure from that field position deep in the Argentina 22 though, finally making territorial inroads pay. Billy Vunipola and Youngs cut open from the scrum and fed Cokanasiga scything off the blindside wing, for a well-worked try.
But again and again the handling errors let England down. Boffelli kept gobbling up the shots at goal, and though England went into the break ahead on the scoreboard, the home men did so with plenty to put right and to prove.
Just when England expected to tidy up their act after the restart though, Argentina were the ones to up the ante.
Santiago Carreras’ smart midfield runaround caught England cold in the backline, with Boffelli searing into the corner from the resulting space.
The wing fluffed his lines off the tee for once, but Argentina were back on the scoreboard again in a flash.
Farrell failed to find Billy Vunipola with a midfield pass, Santiago Carreras stepped through, scooped up – and still had the pace and presence of mind to stride clear and score. Boffelli added the conversion this time, and all of a sudden Argentina were 24-16 ahead.
England needed something, anything, and fast. And Leicester half-back Van Poortvliet jumped off the bench to provide that spark with his first touch.
The savvy half-back cut through the fringes and raced away to score. Farrell’s conversion might have left Argentina leading 24-23, but England were back in the battle and with the final quarter still to come.
Farrell’s fourth penalty gave way to Boffelli’s fifth, a booming effort from almost halfway. That left the Pumas 27-26 ahead, but with England still hunting a grandstand finish.
Farrell landed a tricky effort after Argentina strayed offside at the ruck, for a 29-27 England lead.
Boffelli posted his sixth goal moments later though, after Kyle Sinckler failed to roll away at a ruck. That put the Pumas 30-29 ahead with less than ten minutes to play – and the visitors far the happier to keep trading three-pointers tit for tat.
England were simply unable to get out of their own half for the closing moments, leaving Argentina to add to their Twickenham triumph of 2006 with another major scalp for Cheika’s potent Pumas.