Bermuda, Scotland and Canada also qualified for the West Indies tournament in 2007.
Ireland went into the game knowing only a heavy defeat and a big win for Bermuda over the USA would scupper their bid to reach One-day cricket's premier tournament.
After winning the toss and electing to bat, Ireland were all out for 222 before bowling out the Danes for 149 to claim victory.
Bermuda came into the ICC Trophy as the bottom-ranked of the three participating teams from the Americas region but guaranteed a place at the finals with a 113-run defeat of USA.
With the Scotland versus Holland match at that stage still in the balance, Canada knew it could be crucial to their chances of a top two finish for them to bowl out Papua New Guinea cheaply and Umar Bhatti and Don Maxwell made important early breakthroughs.
Mahuru Dai held out for 52 runs as Papua New Guinea edged past the 100 mark. They were all out for 159 but, with Holland losing to Scotland, net-run-rate was no longer an issue and Canada had sealed a place at a second consecutive ICC Cricket World Cup.
All of the group stage matches took place in the north of Ireland. The action now moves to the south where the semi-finals and final will be held. The semi-finals are on Saturday while the final is at Clontarf near Dublin on Wednesday.