Uruguay's result also means hosts Russia, who have won their opening two Group A matches, are through to the next phase with one fixture to spare, while Egypt and Saudi Arabia are both out of the tournament.
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 winner in Rostov-on-Don on Wednesday.
A corner from the left taken by Carlos Sanchez was missed by the keeper, with Suarez on hand to knock home and become the first Uruguay player to score at three World Cups.
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.
Suarez became Uruguay's sixth centurion and the Barcelona forward saw an early effort blocked.
Saudi Arabia initially showed far greater defensive resilience following their hammering at the hands of Russia, only for Al Owais - who replaced Abdullah Al-Mayoof in the side - to gift Uruguay the opener in the 23rd minute.
A left-wing Sanchez corner was completely missed by Al Owais, giving Suarez a simple close-range finish into an unguarded net.
Fernando Muslera had to tip over a long-range drive from Hattan Bahebri, who then missed a fine chance in the box, as Saudi Arabia responded well to falling behind.
The flat feel of the game continued after the interval with both sides struggling to build tempo in hot conditions at the Rostov Arena.
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 winner.
Saudi Arabia have conceded 14 headed goals at the World Cup and it could have been 15, Martin Caceres heading over in the 68th minute from another Sanchez delivery.
Although Pizzi's side had plenty of the ball in the closing stages there was no route to goal as Uruguay held firm easily
Sterner tests await Uruguay and Russia in the last 16, though, with Group A's qualified nations set to face off on Monday in Samara to decide who secures top spot.
Key Opta stats:
- Saudi Arabia have now been eliminated at the group stages in four of the five World Cup Finals they have participated in.
- Uruguay have won all four of their World Cup matches against Asian opposition.
- Uruguay have now kept back to back clean sheets in the World Cup for the first time since a run of three in 2010.
- Luis Suarez has been directly involved in eight of Uruguay's last 15 World Cup goals (six goals, two assists).