Suarez's goal and Uruguay's win also effectively ended Egypt's hopes of fighting its way back into contention for a berth in the Round of 16, meaning Mohamed Salah's World Cup looks set to end after just three matches.
Saudi Arabia gave a far better performance than they produced in their 5-0 loss to the hosts but a poor mistake from replacement goalkeeper Mohammed Al Owais handed the South Americans the victor in Rostov-on-Don on Wednesday.
The South Americans take on the hosts in their final Group A match on June 25 with top spot on the line, while Egypt and Saudi Arabia have been eliminated after both suffered back-to-back defeats.
Muslera will also tie Ladislao Mazurkiewicz as the player to have made the most appearances for Uruguay at a World Cup.
Suarez's goal was by no means pretty, but it did the trick. "It's a attractive moment and we want to enjoy it", Suarez said.
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Given Uruguay's superior talent level, manager Oscar Tabarez could opt to rotate his squad and prevent any key players from picking up any injuries.
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Maybe Saudi Arabia isn't the worst team at the World Cup? Time will tell whether that 5-0 by Russian Federation is evidence of Ruskie excellence or Saudi hopelessness but either way, I would be absolutely astonished if they get through the group.
Uruguay's Edinson Cavani wasted numerous chances, including one in the 14th minute when he skied a half volley over the bar.
Cavani almost made it 2-0 for Uruguay with a solo run through the opposing defence but his attempt was blocked by Saudi Arabia goalkeeper Mohammed Alowais.
The last two World Cups have seen Suarez exit in ignominy.
Suarez, who became the sixth Uruguay player to reach the century mark, tallied the only goal for La Celeste in the 23rd minute in front of 42,678 fans at the Rostov Arena.
Edinson Carvani almost finished the deal in the 86th minute but Al Owais stopped his shot after a Saudi defender lost the ball at the edge of the box.