Denmark created several early chances and went ahead after 24 minutes when Dennis Rommedahl set up Bendtner and Sunderland's new loan signing from Arsenal drove the ball high into the net.
The tall striker added a second goal 20 minutes later when his rasping drive from 30 metres beat Norwegian goalkeeper Rune Jarstein.
The victory means Denmark, Norway and Portugal all have 13 points at the top of the table.
"Our chances to get to the European championship have increased but we still have two important matches to play," Bendtner said, referring to Denmark's October 7 qualifier away against Cyprus and October 11 match at home against Portugal.
Norway's forwards never really got into their stride and the defence left open big holes. One of the Norwegians' better chances came in the 75th minute when John Carew's shot was blocked by Danish goalkeeper Thomas Sorsensen.
Denmark coach Morten Olsen, whose side drew 1-1 with Norway in Oslo in March, said: "I think we are all relieved. I think the players did a top job, fantastic play."
Olsen praised Bendtner, saying: "He is very important, also the way he combines with the rest of the midfield and defenders."
Bendtner said his recent transfer to Sunderland had lifted a weight off his shoulders. "It has been a heavy cloud over my head for more than a year. So getting away [from Arsenal] means a lot to me."
