South Korea captain Son-Heung Min played with a face mask after suffering a fractured eye socket earlier this month, but the Tottenham Hotspur forward was unable to have much of an impact on the game.
Neither side recorded a shot on target during the match according to FIFA -- the first time that has happened in a World Cup game this century.
"We're a very brave team, we're not afraid of our opponents," South Korea coach Paulo Bento told reporters.
"The bottom line is we need to control all moments of the game, knowing we're in a different competition to our qualifiers. But this won't hold us back from what we intend to do. And we showed today we're capable."
Uruguay almost made them regret that in the 43rd minute when Godin rose highest from a Valverde corner and struck the base of the post with a header.
There was an injury scare for Son around the hour mark when Martin Caceres trod on him, but he was eventually able to continue.
Darwin Nunez curled a shot wide in the 81st minute and Valverde produced a rasping shot from distance in the 90th minute which cannoned off the post, but Uruguay could not find a breakthrough.
Information from Reuters contributed to this report.