Suarez, 31, whose previous two World Cups both ended in bans after his infamous 2010 handball against Ghana and bite on Italy's Giorgio Chiellini four years later, took advantage of a goalkeeping error by Mohammed al-Owais to put Uruguay ahead midway through the first half.
Luis Suarez scored the only goal at the Rostov Arena, sweeping in from close range on his 100th global appearance.
Despite securing progress to the last 16, long-serving boss Tabarez, who has now guided the two-time world champions past the group stages at the last three World Cups, admitted his team were below par. Saudi Arabia have also lost their last 12 matches at World Cup bagging just two draws in a total of 14 matches in the competition.
The Sky Blue should have beaten Egypt by a wider margin than they did but Luis Suarez could not finish multiple chances.
Did you see Shaqiri and Xhaka's controversial celebrations against Serbia — Albanian Eagle
The gesture is likely to inflame tensions among Serb nationalists and ethnic Albanians. Kosovo, a former Serbian province, declared its independence in 2008.
Luis Suarez scored the only goal at the Rostov Arena, sweeping in from close range on his 100th appearance for La Celeste.
It was the Barcelona striker's 52nd goal for his country in that century of games.
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. Salah gives this team a slight edge and that should be the difference as they earn the win.
"We have other priorities, more important than worrying about Cavani and Suarez".
Neymar leaves Brazil training session limping on right ankle
He was limping when he talked to reporters after the match, when doctors dismissed anything serious. He felt some pain and went to the physiotherapy, and tomorrow he will train normally.
The Saudis, however, will look to stay alive, but they'll need to come up with a vastly better showing than they had in the opener against Russian Federation, a 5-0 loss.
Saudi Arabia managed to have plenty of early possession, although without looking overly threatening, only to gift Uruguay a 23rd-minute lead.
Safah was less complimentary and said that the Saudi players had let their fans down, adding: "They seemed scared whenever they attempted to score any goals".
"We must recognise that he's a crucial player to our national team because he shows solidarity on the pitch, he has a sense of responsibility and he has that enormous capacity to score goals".
New Zealand Prime Minister Jacinda Ardern gives birth to girl
The announcement on Instagram was fitting for Ms Ardern, who had also announced her pregnancy in January on the social media site. The much-anticipated arrival has gone global, as worldwide media outlets keep track of what is unfolding at Auckland Hospital.
His side play Egypt in their final Group A game next Monday, when only pride will be at stake as the north African side are also heading home after losing twice. That's not exactly the best preparation for a World Cup match against Uruguay.