Once powerhouses, their show at the Gulf Cup is in stark contrast to previous generations.
Gulf Cup: How the mighty Saudi Arabia have fallen in Asian football
That day it was the eighth wonder of the world, a solo run of light, pitter-patter feet, a turn of pace, a smidgen of luck and plenty of audacity; the kind of 11 seconds that change not just the life of an individual, but, conceivably, the course of a nation.
But Saudi Arabia scored four other goals during their remarkable run to the second round and two of them are worth remembering again.
The first was Fuad Amin's winner against Morocco. He grappled for and won the ball in his own half, shrugged off an opponent and shot from 35 yards, maybe more. Morocco's captain and goalkeeper Khalil Azmi did not distinguish himself in trying to save it, but the shot did swerve cruelly late.
The other was Fahad Al Ghesheyan's goal against Sweden in the second round. Released down the right, Ghesheyan (who would later briefly play for the Dutch side AZ Alkmaar) strode wide into the penalty area.
His second touch with his right foot set it up, a swift change of direction to turn the defender inside out and take the ball to the right corner of the five-yard box, from where he smashed past Thomas Ravelli with his left.
Both goals spoke highly of a wondrous footballing culture of great individual skill, unusually good touch and a fertile attacking imagination (defensively, not so much).
The Green Falcons were every bit as audacious as Al Owairan's goal and in a tournament of pretty audacious goals all round they stood proud.
Those goals and performances remain an apotheosis for Arabian Gulf football; an indicator for where that style of swift, attractive and counter-thrusting football perpetrated by smaller players can take them.
And it is up there with the greatest Asian performances of all time, as good as North Korea's run in 1966 for sure; given how controversial South Korea's last-four finish at home in 2002 ultimately became, perhaps even that.
The point of remembering this is to remind yourself that Saudi Arabia was once a mighty footballing nation, and that 1994 was not just some weird kink in the time-space continuum. It was the work of a nation that made five consecutive Asian Cup finals from 1984 to 2000 (and won it three times) and qualified for three consecutive World Cups after 1994.
A reminder that they once were not what we saw in the Gulf Cup on Monday, in an incoherent 2-0 loss to Iraq. A few years ago, Yemen - their opponents tonight - would be a three-point guarantee. Not now.
It is difficult to know in such an impenetrable culture exactly what has gone wrong. It is easy to point out how quickly they go through managers.
But it is not so easy to square how many coaches they went through between 1984 and 2006 - 32 - with the fact of their success in that golden age.
Was it just the flowering of one golden generation? Not really, because the span of their preeminence was over more than one generation (and the real golden generation came from the Under 17 World Cup winning side in 1989).
And in a country as large as that (at 28 million people, only Iraq in the Gulf Cup has a larger population), quality should be more sustainable than just the serendipitous coming together of a clutch of talented players.
Very broadly speaking, the socioeconomic conditions are conducive too.
There is less reason to worry, as Albert Benaiges, the Al Wasl academy head and once of Barcelona, does in the UAE, for instance.
The standard of living is high for players here, Benaiges says, so that the hunger to use football to transcend circumstance is less, or worse, unnecessary.
In Saudi Arabia, this is not the case. In the 80s and 90s, the hunger for football was evident all around, in empty, sandy plots, apartment buildings, streets, school playgrounds.
In the absence of a ball, many games were played with crushed soft drinks cans (a hint, perhaps, at why ball control among Saudi players is so exceptional but also why sometimes, individual skill trumps team play).
Keener observers suggest that the country has not invested enough into younger talent, or certainly not as much as they used to (their last appearance in the final of the Under 19 Asian Cup was in 1992).
The only truth is that Saudi Arabia, the home of Majed Abdullah, Al Owairan, Sami Al Jaber, Saleh Al Naeema and countless other Asian giants, stands now on the precipice of mediocrity, 1994 but a vanishing dot in the horizon of collective memory.
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