Argentina looked to have rescued a point having come from two goals down when Cristian Medina headed home in the 16th minute of second half injury-time.
However, crowd trouble in the Stade Geoffroy-Guichard halted proceedings, with referee Glenn Nyberg taking both sets of players off the pitch.
The game was subsequently suspended for nearly two hours and once it resumed, the controversy and confusion continued.
Following a VAR review, Bruno Amione was adjudged to have been in an offside position in the build-up to the potential equaliser as Morocco's advantage was reinstated.
The remaining three minutes of the contest played out in front of an empty stadium, with Tarik Sektioui's side able to hold on for an unlikely triumph.
The game finished more than four hours after it started, leaving Mascherano furious at full-time, describing the outcome as not befitting an event as prestigious as the Olympics.
“The match was suspended for security and safety,” Mascherano began. “At no moment did we talk about the review. The official Olympic page put the match at 2-2.
“The match was suspended for security. At no moment did we talk about the review. Then after we were not told anything new, we started to hear things.
“The referee never came, he never gave us an explanation.”
He added: “We turn the page and stay with the positive things from the team in the second half and look for the two wins we’re going to need.
“What happened on the pitch was a scandal. This isn’t a neighbourhood tournament, this is the Olympic Games.
“How are they going to stop the match seven times in the second half because someone comes onto the pitch?
“The second and third time you have to take a decision. Seven times people came onto the pitch.”
Lionel Messi, who won gold for La Albiceleste in Beijing in 2008, also shared his frustrations with his former Barcelona team-mate.
The 37-year-old kept it to the point, posting “Insolito” on his Instagram story, which translates to “unbelievable".
Argentina face Iraq in their next game in Lyon on Saturday, concluding their group campaign against Ukraine on July 30.
Morocco looked set to open their Group B campaign with a memorable win when Al Ain striker Soufiane Rahimi scored twice in a five-minute spell either side of half-time.
However, substitute Giuliano Simeone halved the arrears for Javier Mascherano's men, who twice hit the woodwork before Medina nodded home with the final contribution to an incredible game.
Morocco inched ahead two minutes into first-half stoppage time, Ilias Akhomach bamboozling the Argentina defence with a wonderful backheel that allowed Bilal El Khannouss to cross for Rahimi to tap home.
Within four minutes of the restart, Morocco had a chance to double their lead as the tricky Akhomach was pushed inside the area by Julio Soler. Rahimi stepped up to the spot and made no mistake, stroking his kick into the bottom-left corner.
Mascherano's team dragged themselves back into the contest with 22 minutes to play, though, as Soler's cross-shot was prodded in by the stretching substitute Simeone.
The Albiceleste struggled to carve out clear-cut chances to equalise, but Medina saved the day in dramatic circumstances with 116 minutes on the clock.
Munir Mohamedi spilled Thiago Almada's long-range shot then tipped Bruno Amione's follow-up onto the woodwork. Nicolas Otamendi then looped his header against the crossbar but Argentina made sure at the fourth attempt as Medina nodded into an unguarded net.
Data Debrief: Albiceleste leave it late
Medina's leveller was officially timed at 105 minutes and 24 seconds, the lengthy period of stoppage time a result of several heavy challenges and a number of supporters encroaching on the playing field throughout the match.
Few could argue they did not deserve their point, though, having ended the game with a tally of 2.41 expected goals (xG) to Morocco's 1.46.
Jean-Philippe Mateta's fifth minute strike proved to be the difference in Bordeaux, but ugly scenes at Ilgiz Tantashev's full-time whistle overshadowed Les Bleus' triumph.
Tensions between the two nations had been at boiling point after Argentina's Copa America winning squad were filmed singing a racist chant aimed towards the French.
Argentina's Marco Di Cesare set the tone in a feisty encounter early on, picking up the first of 10 yellow cards shown in the match.
After the Olympic hosts had confirmed their place in the semi-finals, celebrations spilled onto the pitch, which sparked a reaction from the Albiceleste players.
Enzo Millot, who had been substituted five minutes before full-time, received a red card for his actions, much to the frustration of his head coach.
"I don’t agree with what happened at the end of the match. My player [Millot] got a red card and I don’t accept it, it shouldn’t happen," Henry said.
"I couldn’t control what happened. I went to greet the coach and when I turned around, what happened, happened.
"We won, but I didn’t like what happened at the end with my player.
"We don't take this match as revenge because the World Cup was with other teams, Henry continued. "Having scored the goal quickly gave us a decision.
France will face Egypt in the last four of the competition, with the opportunity to win gold for the first time since Los Angeles 1984.
Alvarez, who is currently at the Copa America, was included in Javier Mascherano's 18-man squad as one of the three overage players, along with Geronimo Rulli and Nicolas Otamendi.
The final of that competition takes place just 10 days before the Olympics begins, with Mascherano’s side playing Morocco, Iraq and Ukraine in the group stage in France.
With the Olympics final to be played on August 9, the day before Manchester City's Community Shield fixture against Manchester United, Alvarez's involvement has almost certainly ruled him out of the start of the new season.
Last season, the 24-year-old made 54 appearances in all competitions for Pep Guardiola's side, more than any other player.
Manchester City's Premier League campaign starts on August 18th against Chelsea at Stamford Bridge.
Claudio Echeverri has also been included in the squad. The teenager joined the Premier League champions in January but immediately returned to River Plate on loan.
Sergio Gomez has also been called up by Spain for the competition, meaning Guardiola has three players competing at this summer’s games in Paris.
Argentina looked to have salvaged a 2-2 draw from 2-0 down in Saint-Etienne, with Soufiane Rahimi netting twice before Giuliano Simeone pulled one back for La Albiceleste.
Medina appeared to have equalised when he nodded home following a goalmouth scramble 16 minutes into second-half stoppage time, but crowd trouble then broke out with cups, bottles and pyrotechnics being thrown at Argentina's players by spectators.
The referee took the teams off the pitch, and amid confusion over whether the final whistle had sounded, it was reported another three minutes would be played in an empty stadium.
It was subsequently announced Argentina's potential leveller had been ruled out after a VAR review showed Bruno Amione was offside in the build-up.
Another three minutes of stoppage time were then played out around two hours after the players had been taken off, with Morocco holding on to win 2-1.
While Morocco now sit top of Group B with three points, Javier Mascherano's side – who were among the pre-tournament favourites – remain on zero.
