The Scandinavians, who topped the podium at the Beijing 2008 Games, were slow starters in the tournament, struggling in the early stages, but they saved their best until last and emerged triumphant in a tight match, inspired by Linn Jorum Sulland's 10 goals.
It continues their domination of the women's game as the gold medal at London 2012 adds to the European and World Championships Thorir Hergeirsson's side have won over the last 18 months.
Katarina Bulatovic almost single-handedly kept Montenegro in the game with 10 goals, taking her tally to a superb 53 for the tournament, but it was in a losing cause.
Earlier in the day, Spain claimed bronze by edging out the Republic of Korea 31-29 after double extra-time.
The Europeans, whose previous best-placed finish at the Games was sixth in Athens eight years ago, were on course for a comfortable win midway through the second half, leading by four goals, but a strong Korean fightback forced extra-time with the score tied at 24-24.
After nothing could separate the two teams after the first period of two five-minute halves, another one was forced and Spain finally got the win when Jessica Alonso threw in with 10 seconds remaining to give them a decisive two-goal advantage.