Nani double gives Bento winning start
"I'm naturally very satisfied with a good result, a strong display and that our team was solid for almost 90 minutes," Bento said.
The coach replaced Carlos Queiroz, who was sacked last month for insulting anti-doping agents, and was under immediate pressure after Portugal had begun the campaign with a 4-4 draw against Cyprus and by losing 1-0 to Norway.
The home team looked disjointed in the first half-hour, failing to create chances against a compact Danish defence.
However, once they finally created a flowing move they were rewarded with two quick goals.
Captain Cristiano Ronaldo broke down the left wing and crossed for Nani to fire in a low drive on 29 minutes.
Christian Poulsen then received the ball from the kickoff but underhit his pass and Nani sprinted towards the penalty box to score his second with a thunderous shot.
"They were moments of inspiration. I was very focused on this game, the chances appeared and I was glad to take them and help the team," said Nani, who missed the World Cup in June with a shoulder injury.
Denmark coach Morten Olsen said his players reacted badly to the two first-half goals.
"We controlled the start of the game but then gave the opponents two chances and it changed completely. We became nervous and none of our players seemed to want the ball," he said.
The Danes received a further blow when keeper Thomas Sorensen had to go off with a recurrence of an elbow injury.
Substitute Anders Lindegaard flew through the air to palm away a powerful Ronaldo drive in the 42nd minute.
The Real Madrid striker went close again 12 minutes later when he sent a shot crashing against the bar.
Denmark pulled a goal back as Ricardo Carvalho deflected a corner into his own net after 79 minutes but Ronaldo calmed Portuguese nerves by shooting home with five minutes to go following a Nani pass.
"We dominated almost the entire game, excepting a very short period after Denmark's goal," Bento said. "But even then we didn't lose control and given the number of chances we had we could have scored more."
Portugal are five points adrift of leaders Norway who earlier beat Cyprus 2-1.