Silkeborg generally dominated the match against Akureyri and also produced the majority of chances.
However, the home side had to wait 40 minutes to make their dominance tell as the Icelandic defensive wall finally caved in.
After controlling a pass from Pelle Mattson, New Zealand international midfielder Callum McCowatt launched a terrific long-range stinging drive from outside the box into the far upper right corner to give the home crowd something to cheer about in a generally disappointing first half for the Danish favorites.
However, the Icelandic visitors, who had the former Lyngby player Marcel Romer in their starting line-up never gave up.
After around an hour's play, Akureyri's striker Asgeir Sigurgeirsson came close to equalizing with a close-range effort, but the ball went just past the post.
It looked like Silkeborg were heading for a narrow win which would have put them in the driving seat before the return leg in Iceland in a week's time but it didn't work out that way.
The 34-year-old Icelandic striker Hallgrimur Steingrimsson was allowed time and space to control a long-delivery into the Danish box one minute into injury time time and hammered the ball into the far left hand corner without any chance for the helpless Silkeborg-keeper Nicolai Poulsen.
Should Silkeborg still manage to advance into the third qualifying round for the Conference League, the Jutland team will face the winner of the match between FK Novi Pazar from Serbia and Polish outfit Jagiellonia.