The sides are joined in Group D by defending champions France and Australia, and this clash was seen by many as a chance for either side to prove their credentials as a team worthy of a place in the knockout stages.
But neither could break the deadlock at the Education City Stadium, with Denmark goalkeeper Kasper Schmeichel pulling off a fine save after Issam Jebali went through one-on-one in the first half.
Up the other end of the pitch, Christian Eriksen was denied by a decent stop and Andreas Cornelius somehow missed a header from a yard out.
Here is how the Denmark players rated in their Group D opener:
Kasper Schmeichel - 7
Denied Jebali with a terrific save when one-on-one, the stop being described somewhat hyperbolically by ITV commentator John Hartson as “one of the best I’ve ever seen in my life”.
Joakim Maehle - 7
The left-back threatened on his flank at every opportunity, with some determined runs, neat interplay and threatening crosses. Perhaps should have been awarded a penalty in the final 10 minutes after a couple of deft and clever touches in the Tunisia box.
Joachim Andersen - 5
Was a threat from set pieces but was caught out by numerous Tunisia breaks, as were his colleagues in central defence.
Simon Kjaer - 5
The captain should have done more to ensure that his team’s high defensive line was adjusted, after Tunisia broke through one-on-one multiple times. Was taken off with just over 20 minutes of normal time to go.
Andreas Christensen - 7
Used his face to block a fierce shot from Youssef Msakni in the early moments, before needing a minute to gather his senses. Later made an important interception to stop a cut-back during a promising Tunisia break.
Rasmus Kristensen - 5
The space he vacated by surging up the right flank was exploited by Tunisia at times, and that space wasn’t worth Kristensen’s lack of end product.
Thomas Delaney - 4
Anonymous for the most part, with Denmark’s better moves bypassing the midfielder. Was substituted just before half-time after injuring himself in a challenge.
Pierre-Emile Hojbjerg - 6
Was clearly motivated to get ahold of the game for Denmark, which he tried to do with some switched passes and eager tackles. Had mixed results, however.
Christian Eriksen - 7
Showed throughout the game that his touch, vision and delivery exceed those of any other player involved here. His teammates were unable to convert any of the chances he created, though. Almost put the ball in the top corner in the second half but was denied by a fine save.
Kasper Dolberg - 6
The forward pressed keenly in a bid to make the Tunisia midfield and backline uncomfortable. Was substituted on 68 minutes.
Andreas Skov Olsen - 6
In the first half the winger couldn’t quite time his runs effectively, and his final product was also lacking. He improved after the break, though, and did drill a fine finish into the bottom corner – but the goal was ruled out for offside. Was replaced on 68 minutes.
Mikkel Damsgaard - 6
Replaced Delaney on 45 minutes and played a much different game than his teammate, playing higher up the pitch and making energised runs.
Andreas Cornelius - 4
Somehow failed to score with a stooping header from a yard out.
Mathias Jensen - 7
Was lively from the moment he came on and knitted together some decent passing moves.
Jesper Lindstrom - 6
Put in a solid showing but could not make enough of a difference to change the game.