Suarez celebrated his 100th global cap with the only goal in a 1-0 victory over Saudi Arabia at the Rostov Arena.
The team has now been eliminated from group stages in their four consecutive appearances in World Cup finals since their best in their debut in 1994 when Saudi Arabia had reached the last 16.
The Barcelona striker snatched the game's only goal in the 23rd minute, as Carlos Sanchez's corner delivery found him unmarked inside the six, perfectly teeing Suarez up for the simplest of left-footed volleys.
Paris Saint-Germain striker Edinson Cavani started alongside Suarez as the pair look to add to their combined tally of 93 worldwide goals.
Sanchez and Suarez wasted half-chances to extend the lead for Uruguay, who also won their opener against Egypt 1-0 thanks to a set-piece goal, defender Jose Gimenez heading home a late victor.
The contest continued in similar fashion after halftime as Saudi Arabia pressed forward in search of the equaliser, while Uruguay were content to sit back and pump balls forward in hope that either Suarez or Edinson Cavani could capitalise. 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.
The 71-year-old Tabarez is the oldest coach at the tournament and also led Uruguay to the World Cup semifinals in 2010.
"Of course we demand a lot more from this type of player", Tabarez said at his post-match press conference. They are the only team I have seen so far who had nothing going for them: lumpen centre backs, no pace, no invention, no clue really. But they were outmatched by the Uruguayan defence and were under regular threat from Suarez and Cavani.
The two-time world champions can book their place in the last 16 with victory, while defeat would see Saudi Arabia eliminated after their 5-0 opening thrashing by Russian Federation, while also knocking out Mohamed Salah's Egypt. "Even when he doesn't play well, he always believes he can make a contribution for the team". "My aim is to stay on and to see this team grow".
"We are anxious to change our image, we need to forget our problems and focus on the positive elements to bring happiness to the hearts of the Saudis", said Al-Jassim.
"The difference between the performance in the first game and this game is enormous", Pizzi said.
"We wanted to win and to progress to the knock-out stage and this game simply showed how hard it is". "That's what I know".