It was something Premier League top scorer Robin van Persie never got close to as he came to symbolize Dutch futility with a couple of bad mistakes.
Denmark goalie Stephan Andersen made several clutch saves to secure the most important Danish victory over the Netherlands since the Euro 1992 semifinals.
The Dutch came closest to scoring when Andersen gave away the ball to Arjen Robben just outside the area in the 36th minute, but the Bayern Munich winger curled his left-footer onto the far post and out of danger.
"Five of us had chances," Van Bommel said. "Once we hit the post. So many good opportunities."
Germany beats Portugal
In an earlier Group B game in Lviv, Ukraine, Mario Gomez headed in the lone goal for Germany in its 1-0 victory over Portugal.
Gomez was moments away from being substituted, with Miroslav Klose already waiting on the touch line, when he rose to knock in a deflected cross from Sami Khedira in the 72d minute.
Germany coach Joachim Loew delayed the substitution and Gomez nearly got another goal before Klose finally came on in the 80th and got to play on his 34th birthday.
Racism and violence involving Russia's fans marred the start of the European Championship and confirmed fears that Euro 2012 could be a troubled tournament.
Fans of cohost nations Poland and Ukraine had been seen as a potential source of racial abuse, but Russia has emerged as the main security issue after evidence surfaced Saturday of incidents at Warsaw's Wroclaw Stadium, where Russia beat the Czech Republic, 4-1, on Friday.
Russia supporters later fought stadium stewards in an attack seen worldwide after footage circulated online. Police said four people were treated in a hospital. And Czech defender Theodor Gebre Selassie, who is black, was the target of racial abuse, UEFA said.
On Saturday, UEFA said in a statement it "has opened disciplinary proceedings against the Football Union of Russia for the improper conduct of its supporters."
A potentially volatile clash between Russia and Poland looms in Warsaw on Tuesday - a Russian national holiday with fans planning to march from the city center to the stadium.
A Russia team spokesman, Nikolai Komarov, told the Associated Press in an interview: "The federation has many fans, you don't have control over them all."
Messi's hat trick
Lionel Messi scored on three dazzling runs for his second international hat trick, in Argentina's 4-3 win over Brazil in an international friendly Saturday in East Rutherford, N.J.
With Brazil using a mostly young squad ahead of the Olympics, Messi scored in the 31st and 34th minute on spectacular dashes that beat the defense. Then with six minutes to go, Messi picked up the ball at midfield, dribbled and unleashed a left-footed shot from 21 meters that went in just under the crossbar, delighting a sellout crowd of 81,994 at MetLife Stadium.
Mexico beats Guyana 3-1
Carlos Salcido and Giovani dos Santos scored in a five-minute span early in the first half as Mexico opened World Cup qualifying with a 3-1 win Friday night over Guyana in Mexico City's Azteca Stadium.