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.
Russia and Uruguay will face one of the top two from Group B in the last 16 — either Portugal, Spain or Iran.
The 31-year-old Suarez, 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.
Oscar Tabarez’s side missed plenty of opportunities to add further goals, but a toothless Saudi outfit never seriously looked like snatching a point.
Uruguay, semi-finalists eight years ago in South Africa, have now reached the knockout stage for the third straight time, while Saudi Arabia will try again in their search for a first World Cup win since 1994 in their final game against Mohamed Salah’s Egypt.