The result is, without question, one of the tournament's greatest-ever shocks which has left their place in this year's World Cup in jeopardy.
The much-fancied Argentines, second favourites to lift the trophy going into their opener in Qatar, were in total control at the break after Lionel Messi opened his account from the penalty spot.
But the Gulf state were transformed after the interval and flipped the game on its head with two goals in the space of five minutes, Saleh Al-Shehri levelling with a low effort and Salem Al Dawsari scoring a peach of a winner.
There was absolutely no sense that we were on the cusp of watching one of the World Cup's greatest upsets when Lionel Messi put the Albiceleste in front from the penalty spot.
His 10th minute spot kick – a vision in cool, incidentally, as he casually sent the keeper the wrong way – was his seventh World Cup goal and any concerns about the little maestro's fitness looked completely misplaced.
The 35-year-old, who had already drawn one save from the keeper before his opener, was at the heart of everything good about Argentina as they sought to put their 51st-ranked opponents to bed by half time.
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They had another three efforts disallowed for offside as they repeatedly tried to break Saudi Arabia's high line, and those misjudgements would go on to prove costly.
Within 10 minutes of the restart, the Saudis, still gambling defensively but more proactive in attack, had beaten Emi Martinez twice leaving the shellshocked Argentines half an hour to avert a disaster.
And that's when their cool went, their class disappeared and they suddenly looked ordinary outfit against an opponent – 14/1 shots lest we forget – who were throwing bodies everywhere in an heroic effort.
Argentina doubtless never thought they'd rue those disallowed first-half goals.
This was a team who had arrived in the Gulf on a 36-match unbeaten streak, a sequence that had taken in glory at the Copa America, and they just don't concede goals.
On top of that, Messi was fit and ready to spark the world's second-ranked team into life, overpowering the Saudis ahead of supposedly sterner tests against Poland and .
What was astonishing, however, was that having cut the Saudis apart time and again in the first 45 minutes, they did it hardly at all in the second period as the inspirational well ran dry.
Messi was given no space, inevitably, but the likes of Rodrigo De Paul, Angel Di Maria and Alejandro Gomez simply failed to turn up, the odd decent cross, the occasional well-timed pass woeful returns over 100-plus minutes in which the odds-on shots mustered just six efforts on target, most relatively tame.
Now they have been eased to 8/1 to go all the way and may not have too many takers even at that price.
Parallels with 1990 are obvious. Back then Argentina went into their opener at Italia '90 as the defending champs and duly lost 1-0 to a side, who kicked them into submission.
The Saudis weren't quite that ruthless but they didn't back off as a haul of six yellow cards testifies, before they were able to celebrate their greatest ever result which saw them cut to 350/1 to win the tournament.
Argentina are now 8/1 ahead of a daren't-lose showdown with Mexico on Saturday night that has suddenly become critical. Lose that and their World Cup could be over less than a week after it had started.
Despite the defeat, Lionel Scaloni's South American champions were still 8/15 to qualify from Group C and 13/8 to win it – (the Saudis, should you be tempted after their magnificent first effort, are 7/2 to win the section).
As for thinking the unthinkable, Argentina are 9/1 to finish bottom of their group.
And what of Messi, the Diego Maradona of this generation, the player who has to tick for Argentina to do well?
Well, he went in for first-scorer punters with his seventh World Cup goal, and joins an elite group of players, including Pele and Cristiano Ronaldo, to have scored at four different finals.
And he's 4/11 to be Top Team Goalscorer for Argentina and for Top Goalscorer outright.
But many punters and fans were asking at the final whistle whether this might be one challenge too far for the 35-year-old – yes, 35 – who has carried the hopes of his nation on his shoulders so manfully for a decade and more.
On Saturday night, at the same , against Mexico, maybe we'll find out.
Steve Freeth looks at how Tuesday morning's result has affected the betting.