Suarez's 52nd worldwide goal means that Uruguay and Russian Federation have both qualified for the knockout stages of the competition, while Saudi Arabia and Egypt are eliminated with one group match still to play.
Luis Suarez scored the only goal at the Rostov Arena, sweeping in from close range on his 100th global appearance.
But their hard work was undone by some poor marking in the 23rd minute as Suarez became the first Uruguayan to score in three successive World Cup finals with the opening goal.
"I think Uruguay were happy to win 1-0 today, but I think they will improve". He fell back to defend and raced forward on the counterattack.
"Well, as for the event yesterday [Monday], you've seen the pictures, they speak for themselves, but we don't know anything else, we have had no further info", he said.
Saudi Arabia were dealt a blow just before half-time as Hussain Almoqahwi replaced the injured Taiseer Aljassam following a coming-together with Suarez.
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"We have other priorities, more important than worrying about Cavani and Suarez".
"We've done everything we could for the national team players", he thundered, before adding: "They've blackened my face".
Saudi Arabia's last outing against the host was nothing less than a horror show, 5-0. This bet is tight but we believe the under is the best pick.
Uruguay's victory means long-serving coach Tabarez has guided them out of the World Cup group stages in three successive tournaments.
"But we'll still represent our country, and we'll make Saudi Arabia proud even though we are out of the tournament".
In the 86th minute, Cavani got a chance for a second for Uruguay as he picked up the ball on the halfway line and ran it all the way into the box, but was stopped by the Saudi defense. He also has nine goals in his last nine starts for Spain.
Suarez threatened with a free-kick which was theatrically repelled by Al Owais early in the second period, before Carlos Sanchez wasted a free header following a fine cross from Edinson Cavani.