Godin, who was making his 117th worldwide appearance, sent a free kick from the right into the area.
A poor contest looked likely to end in stalemate but with Uruguay cranking up the pressure late on, Atletico Madrid's Gimenez rose to power a header into the top corner and break Egypt hearts.
Meanwhile, NAIJ.com had earlier reported how the Russian national team dismantled Saudi Arabia in the opening match of the tournament.
Egypt play Uruguay - tipped by some to be dark horses - in Yekaterinburg in just the second game of the tournament, following Russian Federation against Saudi Arabia in the opening match.
Uruguay's forward Luis Suarez (left) fires the ball into the side netting missing a chance during their Russian Federation 2018 World Cup Group A match against Egypt at the Ekaterinburg Arena in Ekaterinburg on June 15, 2018.
It would be a shame if the Premier League's best player and Ballon d'Or dark horse Salah can't go.
The tournament in Russian Federation will be the poorer for Salah missing out and Uruguay goalkeeper Fernando Muslera has expressed hope that Salah will play against the South Americans. I think Egypt are a good team.
La ciencia recreó el rostro de Dios según los creyentes
Las personas que informaron que eran más atractivas físicamente también creían en un Dios más atractivo físicamente. La gente imagina un rostro más joven, más femenino y menos caucásico de lo que sugiere la cultura popular .
The Pharaohs were issued a real scare when Cavani forced another world-class save from El Shenawy and hit the post in quick succession - going into the last ten minutes of the encounter.
"In the history of football we have broken a spell", said Uruguay coach Oscar Tabarez. It managed two draws at the 1990 tournament and left empty handed in 1934.
With a nation sweating on his fitness, manager Hector Cuper has relieved these stresses and confirmed that Salah is "almost 100%" certain to play against Uruguay.
"Suarez even playing not as well as normal had three goalscoring opportunities and the Egypt keeper saved a couple of them so that's to his credit", Tabarez said.
With its traditional defensive tactics preferred by Cuper, Egypt badly needs Salah and his goals to succeed.
The result sees the South Americans draw level with Russian Federation on three points at the top of Group A.
It was hardly a convincing Uruguayan performance despite the win.
The clash between two of Russia's rivals to reach the knock-out stages failed to capture the imagination of football fans in the country, as FIFA's decision to charge as much as £300-a-seat came back to haunt them.
Egypt offered little in Salah's absence and are now under pressure heading into a clash with Russian Federation, while Uruguay - and particularly Suarez - can breathe a sigh of relief. They were impressive at the 2010 World Cup, where they finished fourth.