They suffered no shortage of setbacks in the build up as Sean O'Brien was handed a ban while Paul O'Connell, Peter O'Mahony and Jonathan Sexton were all rued out injured - the latter just 24 hours before kick-off.
British & Irish Lion Tommy Bowe joined the casualty list before the quarter-hour mark but not before tries from Matias Moroni and Imhoff had opened up a 14-0 lead for Argentina.
Luke Fitzgerald stopped the rot with a superb try before setting up Jordi Murphy early in the second half but late scores from Joaquin Tuculet and Imhoff secured a deserved victory over the reigning Six Nations champions.
Argentina struck after just three minutes, spreading the ball to the right touchline where Moroni found enough space to dash over the line, Nicolas Sanchez converting.
And they were soon further ahead when Imhoff won the race to Santiago Cordero's chip, Sanchez's second conversion - which bounced in off the post - leaving Ireland with an early mountain to climb.
It got worse three minutes later when Bowe was forced off injured and Mike Ross was caught off his feet at the ruck, allowing Sanchez to make it 17-0.
If the All Blacks were at their fluid best the night before, Argentina weren't far off but a late tackle with the shoulder soon earned Ramiro Herrera a spell in the sin bin.
Ian Madigan then skipped over after a quick-tap penalty but referee Jerome Garces called the play back and the Irish fly-half pointed to the posts, tapping over to put his side on the board.
And they were punished almost immediately when replacement Fitzgerald - who toured South Africa with the British & Irish Lions in 2009 - sped away down the left and wrong-footed Tuculet to score, Madigan converting.
Madigan was next to hit the post with a penalty, leaving them ten points behind at the break, but Ireland started the second half on the front foot and struck early.
Fitzgerald was involved again, powering through a gap in the Pumas line and finding flanker Murphy with a neat one-handed offload, while Madigan added the extras.
Sanchez struck another penalty between the posts but Madigan soon replied in kind after Herrera narrowly avoided a second yellow card for entering the ruck with no arms.
Madigan pushed a long-range penalty wide on the hour mark but Sanchez made no such mistake from close range after Devin Toner's high tackle.
Argentina struck the killer blow ten minutes from time, when the ball went from right to left and Tuculet stretched out to dot down right in the corner.
Imhoff put the icing on the cake, collecting the ball just inside the halfway line and skipping between two defenders to earn a clear path to the line.
Man-of-the-match Sanchez converted both and added another penalty as Argentina put the gloss on a very impressive display.