Scotland led 14-0 at half-time with tries by Jack Dempsey and Ewan Ashmen and a comfortable vistory looked on the cards when Ashman stretched their advantage to 21 points four minutes after the break.
A fourth try beckoned when Finn Russell's long pass was picked off by Rodrigo Isgro, and Blair Kinghorn was sin-binned after Argentina broke into Scotland territory.
Julian Montoya crashed over off the back of the penalty to get Argentina on the board and Gregor Townsend's side never recovered.
Another four tries followed to give Argentina the 33-24 victory.
"We fell asleep at the wheel," Scotland skipper Sione Tuipulotu told TNT Sports after the final whistle. "It's not good enough."
Tuipulotu was asked if criticism from the stands was justified after the defeat and said: "I think so, yeah.
"Gregor has spoken in the changing room about back-to-back home sell-outs, not every stadium does that.
"We watched some rugby yesterday and there were some empty seats in the stadium, but not in our stadium and there's a little bit of guilt there because people pay good money to come watch us."
Scotland went from a commanding position to being carved open almost at will, and were unable to regain any momentum.
Scotland came close against New Zealand last weekend, coming from 17-0 down to level before conceding at the death, but Tuipulotu said this result was the bigger disappointment.
"I don't think I could be as disappointed as I was last week, but I think this is more disappointing," Tuipulotu said.
"I said to the boys, 'We are going to have to take a really hard look at ourselves'.
"The next couple of days are going to hurt and it starts with me, I'm the captain of the squad and I take responsibility as well."