Ada Hegerberg scored just after the break and her sister Andrine scored the winner 11 minutes from time.
Both teams are tied with three points after two games in the group stage. North Korea leads Group C with six points following a 9-0 drubbing of Argentina.
"It was a disappointing result," said Canadian coach Andrew Olivieri. "There were a lot of promising performances, but winning is part of the player development at this level."
Canada will close out the group stage Monday against North Korea. The top two teams in each group advance to the quarter-finals. If two or more teams finish tied on points, goal differential will determine who goes through.
Jenna Richardson scored for Canada in the 44th minute.
Canada created numerous chances in the first half, but couldn't quite hit the target as balls either went wide or into the arms of Norwegian goalkeeper Nora Gjoen.
Nearly midway through the first half, Norway thought it had its chance after referee Qin Liang called a penalty on Canada. Ada Hegerberg took the kick, but her shot to the left was stopped by Canadian goalkeeper Sabrina D'Angelo.
"I think we certainly had the better of the play and chances in the first half," said Olivieri. "Other than the penalty chance (for Norway), we could have gone up by three goals after 45 minutes — so the first half was positive in that sense."
In the second half, the game opened up and Norway got the equalizer in the 52nd minute. Andrine Hegerberg blasted a shot past D'Angelo 15 minutes later for the lead.
"In the second half, we knew we couldn't sit back, we had to keep going forward," said Olivieri. "The game opened up and started going back and forth, perhaps a little more than we would have liked."
Kim Un Hwa scored five goals to lead North Korea to a rout of Argentina, which gave up six goals in its first game against Canada. Kim Su Gyong had a hat trick and Yun Hyon Hi scored the other goal for the 2006 champions.
Meanwhile, in Hiroshima, substitute Lina Magull scored an injury-time winner as defending champion Germany beat Ghana 1-0.
Magull, who came on in the 83rd minute, took a perfect pass from Dzsenifer Marozsan and beat Ghana goalkeeper Patricia Mantey with an angled left-footed shot in the first minute of injury time as Germany improved to six points in Group D.
"It was very exciting to get a goal so late in the match like that," Germany coach Maren Meinert said. "The players worked very hard and were rewarded for their work. Ghana was a tough opponent and we had to think about different formations."
The United States was held to a 1-1 draw by China in Group D's second game of the day, a result that ensured Germany became the first team to advance to the quarter-finals.
Shen Lili scored with a superbly struck drive from the top of the area in the 19th minute and Maya Hayes equalized for the Americans with her fourth goal of the tournament in the 36th. The U.S. has four points and must avoid defeat in its final group match against Germany to definitely advance.
"I thought we played well in stretches," U.S. coach Steve Swanson said. "It's too bad we gave up that early goal which was China's only real chance. This was not the result we wanted but I thought we played well, now we have to just turn our thoughts to the next game."
China, which has one point and still has a chance of advancing, plays Ghana in its last game of the group stage.
- with files from The Associated Press.Suggest a correction