Saudi Arabia, ranked 51st in the world, could have been done and dusted in the first half when Lionel Messi scored from the penalty spot before Argentina had three goals called out for offside.
Saudi Arabia, on the other hand, turned the game on its head in a dramatic 10-minute stretch after halftime, with Saleh Al-Shehri levelling with a low effort and Salem Al Dawsari shooting them ahead to create pandemonium in the stands.
After displaying their ruthlessness on one end, the Green Falcons showed their toughness on the other, fending off an outstanding Argentina front line to record just their fourth World Cup win in history and open up the group.
Argentina, led by Lionel Scaloni, entered the tournament as one of the favourites after going 36 matches without losing, which includes winning the 2021 Copa America.
They now have a lot of work to do if they want to maintain their hopes of winning a first major title since 1986 and give Messi a proper sendoff for what will likely be his final World Cup.
On Saturday, they will face Mexico, while Saudi Arabia will face Poland.