Aberdeen dominated in the first half only to fall into an alarming second-half slump.
Against the run of play, however, they took the lead in the 79th minute when Niall McGinn latched on to a Shay Logan cutback.
Shkendija made the most of the wilting Dons to turn possession in their favour and equalised through substitute Hristijan Kirovski who headed the ball past goalkeeper Danny Ward in the 84th minute, just seconds after coming on.
Dons defender Mark Reynolds could be set for a stint on the sidelines after the 28-year-old fell heavily on his arm and was substituted with a suspected wrist injury.
While conceding a late goal was a defensive lapse, the away goal could prove priceless and the draw will come as something of a relief for Dons manager Derek McInnes who went in to the opening Europa match with little knowledge of his Macedonian opposition.
Shkendija, who won the Macedonian title for the first time in 2011, finished third last season but have failed to win a European tie in three attempts.
However, returning coach Shpetim Duro had added four Macedonia internationals to his squad in the lead-up to the Europa match.
The Dons will look to make the most of their home advantage when they host Shkendija in the return leg at Pittodrie on July 9.