Copenhagen ground out a 0-0 draw at Bayern Munich in their Champions League Group A match on Wednesday to snap their opponents' 17-game winning run in group-stage matches and stay in contention to reach the last 16.
The Bavarians have secured top spot in the group on 13 points, with the Danish side second on five.
Both teams needed time to settle in with Bayern missing several key player through injury.
Copenhagen had an early chance when Roony Bardghji's 27th-minute shot sailed narrowly wide and Thomas Mueller's close-range header for Bayern was saved by keeper Kamil Grabara.
The visitors, whose solid backline has been key to their success this season, defended well and came close again two minutes after the restart through Diogo Goncalves' curled shot.
The Danes can qualify for the knockout stages by beating Galatasaray, who are also on five points after drawing 3-3 with bottom club Manchester United, and they almost snatched a last-gasp winner.
Bayern keeper Manuel Neuer came to the rescue, however, with a double save to deny Elyounoussi and extend the German champions' record unbeaten run to 39 straight group-stage matches in the competition.