The Danes launched a virtual siege on the Welsh goal straight from the start, which resulted in a handful of corner kicks.
The visitors often struggled to clear the ball under the Danish pressure, and it nearly paid off for the Danes, when Pernille Harder sent a header onto the crossbar after few minutes of play.
However, the local spectators in Odense did get a scare after 20 minutes, when Stine Balisager had to clear the ball off the line after a promising Welsh attack on the Danish goal.
But that remained Wales' only effort on the Danish goal in a first half where Amalie Vangsgaard and Harder wasted great chances to turn the Danish dominance into goals on the scoreboard.
Thus it remained scoreless after the first 45 minutes.
The Danish dominance continued after the interval and eventually the Welsh defense caved in shortly into the second half, when Harder unmarked searched past an extremely passive Welsh rearguard before calmly slotting the ball into the net.
The goal gave the Danes a bit of peace of mind, which also meant that national coach Andrée Jeglertz asked his players to take a slightly more defensive approach allowing Wales to regroup.
The Danes, however, still managed to create chances and the hosts nearly doubled their lead with 20 minutes to go, when a close-range effort by Vangsgaard was cleared off the line.
Towards the end, Wales pushed the Danish women far back, but Denmark looked well composed defensively and can now look forward to the group final on Tuesday against Scandinavian rivals Sweden.