Fatos Beciraj was Montenegro's match-winner in their World Cup qualifier against Denmark in Copenhagen.
The Dynamo Moscow forward struck the only goal of the game as Montenegro moved joint-top of Group E alongside Poland following the 1-0 success.
Denmark, who have now suffered two defeats in four days after losing in Poland on Saturday, went close through a Viktor Fischer header but the ball went over the crossbar.
Shortly afterwards Stevan Jovetic set up Beciraj and his rising shot from the edge of the penalty area hit the back of the net.
Mladen Bozovic preserved Montenegro's lead with a decent save to repel Thomas Delaney's well-struck shot and he showed his good form again with 10 minutes remaining to keep out an effort from Tottenham midfielder Christian Eriksen.
Denmark almost salvaged a point two minutes from time when Andreas Cornelius' header struck the crossbar but the visitors held on for a valuable three points.