Luis Suárez opened the scoring from close range after 23 minutes.
Uruguay struggled to assert their authority on the game but the slender victory means they join hosts Russian Federation in the last 16, while eliminating their opponents and Group A rivals Egypt. The defeat means both they and Egypt are eliminated from the tournament after successive defeats.
And there were also moments of promise from Fahad Al Muwallad and Mohamed Kanno without there ever quite being enough thrust or accuracy to trouble their South American opponents or deliver a first victory in 12 World Cup matches.
But Group A favourites Uruguay are still widely expected to clobber Saudi Arabia, the second-lowest World Cup team in the Federation Internationale de Football Association rankings at No. 67.
The goal was special for Suarez, as not only did it guarantee a spot in the knockout stages, it was the striker's 100th cap for Uruguay.
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"We imposed ourselves on the game", said the Argentine coach, who took charge of the Arab nation after they had qualified for their first World Cup since 2006. "It's a attractive moment and we want to enjoy it", Suarez said.
Then the ball was out of reach of Saudi Arab goalkeeper Mohammad Al Owais. They were more functional than exhilarating and reliant upon the threat carried by Barcelona's Suarez and strike partner Edinson Cavani.
Sides such as Saudi qualify for the World Cup via the Asian Football Confederation and Morocco, Egypt and Tunisia via the Confederation of African Football - an Egyptian fan explained that in football, they are "Arab first, Africans second". However, Saudi Arabia bounced back with a much better effort than what we saw in its opener and made things very hard on the South American side.
Queiroz had no complaints about the VAR decision which ruled out Saeid Ezatolahi's strike for offside, preferring instead to rue that it had not been around at the 2010 World Cup when his Portugal were beaten by a contentious Spain goal.
Saudi Arabia managed to have plenty of early possession, although without looking overly threatening, only to gift Uruguay a 23rd-minute lead.
Nathian Nandez and Giorgian De Arrascaeta are dropped in favour of Carlos Sanchez and the 32 year-old Cristian Rodriguez.