Scotland thought they had survived an almighty scare when keeper Lee Alexander saved Florencia Bonsegundo's spot kick in stoppage time but the VAR judged the keeper was off her line before the kick was taken.
Bonsegundo made no mistake with her second effort, sealing a remarkable fightback that left Scotland bottom of Group D and out of the tournament while third-placed Argentina kept alive their slim hopes of making the last 16.
"I'm absolutely gutted for the team," Scotland's Erin Cuthbert, player of the match, told reporters.
"I think we should have put the game to bed. We were on top of the game, but these things happen. It's football. It gives you incredible highs but also incredible lows and we saw that again tonight."
Scotland needed a win to have any chance of getting through and looked to have comfortably sealed victory having taken a 3-0 lead after 70 minutes with goals from Kim Little, Jennie Beattie and Cuthbert.
Argentina should have taken the lead after suffocating Scotland in the early stages and on 17 minutes Mariana Larroquette smashed a header against the bar.
They paid for that miss when Cuthbert burst into the penalty area two minutes later shooting powerfully at keeper Vanina Correa, who saved, but the Chelsea forward reacted quickest to cut the ball back to Little who slid home.
The goal freed the Scots, who appeared fully in control after the restart with Beattie doubling the lead from a Caroline Weir cross.
Cuthbert then looked to have killed off the match in the 68th minute when she reacted quickest to stroke the ball in after Leanne Crichton headed onto the post.
Yet with little to play for Argentina brought on Dalila Ippolito and Milagros Menendez midway through the second half, rejuvenating their toothless attack.
Menendez first slipped home from a through ball by Ippolito and then Bonsegundo's shot on the 74th minute from outside the box crossed the line setting up a grand-stand finish.
A VAR review then confirmed Aldana Cometti was brought down in the 87th minute, but Bonsegundo's poor penalty was initially saved only for the referee to call for the kick to be retaken after consulting the VAR.
Bonsegundo fired home second time round, as Argentina became the first ever side to come from three goals down to avoid defeat in a women’s World Cup match.
"It's unbelievable what can happen in four minutes," Argentina coach Carlos Borrello told reporters.
"We do have a chance now. Getting fresh players on the pitch and finding the right combinations and positions (was key). I'm left with a bitter taste because if we'd given a little bit more we could have won."
Scotland finished bottom of Group D with one point, a point behind Argentina who have a slim chance of qualifying as one of the best third-placed sides.
(Reporting by John Irish; Editing by Toby Davis)
