Copenhagen were outplayed by Celtic but the latter had Fraser Forster to thank for earning them a first-leg draw with a penalty save.
Celtic were the much better side in the first leg of their Europa League last-32 tie against Copenhagen, but the Scottish champions were ultimately grateful to claim a 1-1 draw at Parken thanks to Fraser Forster's wonderful late penalty save.
Neil Lennon's men claimed a deserved lead through Odsonne Edouard on Thursday, having failed to score in their last nine away knockout games in Europe, and looked superior to their hosts for long periods.
However, Dame N'Doye grabbed a 52nd-minute equaliser for Copenhagen and Jens Stage had the chance to seal victory with a penalty awarded with the aid of VAR, only for Forster to tip his spot-kick on to the left-hand post.
Celtic will now be confident of securing progress in next week's return tie in Glasgow, although they may wonder how they did not win this encounter by a comfortable margin.
Edouard was twice denied by Karl-Johan Johnsson inside the first four minutes, the Copenhagen goalkeeper also combining with Ragnar Sigurdsson to keep out a follow-up to the second effort from Olivier Ntcham.
It proved a case of third time lucky for Edouard when he was presented with another chance in the 14th minute. The prolific striker calmly clipped the ball past Johnsson after fine work from Ryan Christie and Callum McGregor.
The impressive visitors remained in the ascendancy prior to the interval, Copenhagen's only effort of the first half coming when Bryan Oviedo curled a shot wide on his weaker right foot.
However, Copenhagen came out for the second period with renewed vigour and they equalised when N'Doye fired home off the left-hand post from Rasmus Falk Jensen's pass after Ntcham had been robbed of possession.
McGregor blazed a shot wastefully over the bar, a Christie cross from the right almost found the far corner and Edouard was again denied by Johnsson as Celtic quickly regained the upper hand.
Copenhagen were given the opportunity to snatch a scarcely deserved win when a VAR review penalised Christie for handball at a corner, but Forster reacted superbly to deny Stage from 12 yards.
At the other end, home goalkeeper Johnsson rounded off a wonderful performance by denying James Forrest at his near post.