Diego Alonso's team twice hit the woodwork through Diego Godin and Federico Valverde, but the South American nation could not find a winner, with the points being shared in Al Rayyan.
La Celeste are next in action against Portugal on Monday, while South Korea will be bidding to record their first win in the 2022 competition when they take on Ghana on the same day.
South Korea were the team on the front foot in the early exchanges, with the movement of their forward players causing problems for the Uruguayan defence, which once again included Jose Gimenez and Godin.
The first real chance of the match came in the 19th minute when Gimenez picked out Valverde with a sensational long pass, but the midfielder's effort was deflected just wide of the post.
Gimenez then picked out Facundo Pellistri with an excellent pass; the Manchester United attacker delivered towards Darwin Nunez, but the forward could not make contact on the ball under pressure.
Led by Son Heung-min, who played in a mask due to his recent facial surgery, South Korea made the stronger start, but Uruguay were looking the most likely as the first period developed.
South Korea did have a golden chance to score in the 34th minute when Hwang Ui-jo found himself free inside the Uruguayan box, but he somehow cleared the crossbar.
Godin then headed against the post from a corner in the 43rd minute, with both sides having excellent chances to make the breakthrough in the latter stages of the first period.
Nunez broke into the South Korean box just past the hour, with Luis Suarez in close attendance, but goalkeeper Kim Seung-gyu did well to clear the ball away from danger.
Edinson Cavani was introduced for Suarez in the 64th minute, and Uruguay were the side looking the more likely to make the breakthrough with the match heading for its final 20 minutes.
South Korea had a chance of their own in the 77th minute when Cho Gue-sung found himself free outside the penalty box, but he dragged his effort just wide of the post, before Nunez just missed the target with a powerful strike down the other end 10 minutes from time.
Valverde rattled the woodwork for Uruguay in the 89th minute, with the Real Madrid midfielder's stunning effort from distance clipping the outside of the post.
Son then struck wide of the target moments later, with a poor kick from Sergio Rochet handing South Korea the chance to secure all three points late on.