Valdet Rama put the home team in front after 41 minutes when he sprinted down the left wing before cutting in to score.
Fired up by Rama's goal and an enthusiastic crowd, Albania could have scored a second when a Hamdi Salihi header was touched on to the bar by Norway goalkeeper Rune Jarstein.
Hogli was then left unmarked to head Norway back on terms in the 85th minute.
Albania, who have never qualified for the finals of a major tournament, have 10 points from six games, one behind group leaders Switzerland.
Norway have eight points from six matches.