Romania appeared to have clinched the points in the European Group E match when substitute Adrian Popa kept his composure to score after the ball was deflected to him in the 85th minute.
Montenegro levelled 90 seconds later when Steven Jovetic headed in Damir Kojasevic's free kick, then Romania were awarded a last-gasp penalty only for Stanciu to send his shot well over the crossbar.
Much-travelled German Daum became Romania's first foreign coach for more than 80 years when he replaced Anghel Iordanescu, who stepped down after Romania's failure to make it past the first round of Euro 2016. "My boys deserved to win if I judge by their efforts and especially by what they did in the second half," he said.
(Writing by Brian Homewood; Editing by Rex Gowar)
