The match started with intensity, with Tunisia putting up a spirited performance as they were cheered on by noisy fans who showed up in large numbers.
Tunisia striker Issam Jebal had the clearest chance of the first half, but Denmark goalkeeper Kasper Schmeichel made a superb save to keep the game scoreless.
The Danes dominated the first quarter of the second half but found it difficult to break their opponents.
Eriksen came close with a 20-yard strike, but Tunisia goalkeeper Dahmen pulled off an impressive save.
Denmark’s Cornelius mysteriously missed from two yards, as a header from a rebound struck the post to the relief of the Tunisian defence.
Despite a late scare of a potential penalty against Tunisia, the referee, Cesar Ramos, decided not to award the penalty as the game ended with both sides sharing the spoils.
The other Group D game would see France take on Australia later on Tuesday.