A Jon Dahl Tomasson double put Denmark in pole position in Group A after the opening round of matches.
The Feyenoord forward struck late in each half to help the Danes take a giant step towards the second phase.
Two excellent goals - one a well-worked team effort, the other an incredible piece of individual technique - looked to have left honours even.
But Tomasson changed the complexion of the group with a deft header eight minutes from time.
Denmark gradually came to dominate the opening period and took the lead just before half-time when Tomasson finished a well-crafted move.
Uruguay equalised immediately after the break with an early contender for goal of the tournament - a fantastic 25-yard volley from full-back Dario Rodriguez.
But AC Milan-bound Tomasson gave the Danes a victory that puts holders France in deep trouble after their defeat by Senegal on Friday.