Suarez came close to doubling his tally in the second half, forcing a diving save from Saudi keeper Mohammed Al-Owais with a 50th-minute deflected free kick.
Suarez celebrated his 100th global cap with the only goal in a 1-0 victory over Saudi Arabia at the Rostov Arena.
Uruguay have only won their first two matches at a World Cup on two occasions prior to 2018, the aforementioned campaign in 1954 and the 1930 tournament where they were the hosts and eventual winners.
With Juan Antonio Pizzi's men unable to create a clear chance, Saudi Arabia are without a win in 12 World Cup matches and in danger of finishing bottom of their group, as they have in all three previous appearances.
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At least Suarez, who missed three sitters in Uruguay's 1-0 opening win against Egypt, was his vintage efficient self with his 52nd global goal although he will not have dismissed fears he was not 100 percent fit.
Saudi Arabia, thrashed 5-0 by Russian Federation in their opener, offered more resilience against Uruguay but rarely threatened an unlikely draw and coach Juan Antonio Pizzi felt his players showed a significant improvement in their performance.
Maybe Saudi Arabia isn't the worst team at the World Cup?
"They've got a lot of good players with a lot of experience, and for a lot of them it could be their last chance at a World Cup".
"We do want to score more but there are other positives: no yellow cards, no injuries", Tabarez said. Many Uruguayan fans do not care what style of football is played or what level the performance is at, so long as the final result is preferable. They were more functional than exhilarating and reliant upon the threat carried by Barcelona's Suarez and strike partner Edinson Cavani.