Scotland had been cruising towards a comfortable home win after scoring three tries in the opening 44 minutes, but five changes off the bench by Argentina altered the outcome in a spectacular turnaround.
Captain Julian Montoya, Rodrigo Isgro, Pedro Rubiolo, Pablo Matera and Justo Piccardo all scored for Argentina after Scotland had gone ahead via Jack Dempsey and two tries for Ewan Ashman.
Santiago Carreras converted four of the five Pumas tries while Finn Russell put over a penalty and three conversions for the home side.
The contrast in performance from one half to the next was stark as Scotland started strongly and scored their first try after 13 minutes with Dempsey sprinting through the Argentina defence.
Darcy Graham’s catch of a high kick set up Scotland’s second try in the 28th minute, scored by Ashman with a burst over the line from close in after several phases of attack.
Ashman then again displayed his strength four minutes into the second half as he powered over for Scotland’s third try. It came after he had initiated a counter from Argentina’s failure to find touch with a clearing penalty from deep in their own half.
Down 21-0, Argentina brought on five substitutes at the same time in the 45th minute to freshen up a listless-looking line-up, but it was a loose pass from Russell that gifted them their opportunity to launch a sensational comeback.
Isgro intercepted and broke away, forcing Scotland to scramble their defence, give away a penalty and see Blair Kinghorn sent to the sin-bin. Argentina took a scrum instead of a kick and punched at the line several times before skipper Montoya went over for their first points, 55 minutes into the match.
Isgro scored a second Argentina try three minutes later after Juan Martin Gonzalez’s initial break, but Scotland temporarily stymied the visitors’ momentum as Russell put over a penalty to put the hosts 24-12 up.
But Argentina got a third try with 10 minutes left as lock Rubiolo forced his way over between the sticks at the end of another display of forward power to cut Scotland’s lead to five. A nervy Murrayfield then went silent as Carreras’ break set up another series of attacks at the home line before Matera scored.
Carreras’ conversion put Argentina ahead for the first time with five minutes left, but they continued their turnaround with a fifth try as Piccardo dotted down in the corner in the last minute.
"It was 21-0 and we have a chance, but pull the trigger too early, but they go up the other end and score two quick tries," said Scotland captain Sione Tuipulotu.
"It is going to be a painful couple of days, but we've got to stick together."
