The hosts took the lead in the 27th minute when skipper Teddy Teuma found the back of the net from inside the box.
In the second half, Dante Vanzeir doubled their advantage after converting a 76th minute penalty.
Rangers will return to Ibrox for the second leg, but will need to produce an almighty comeback if they are to keep their hopes of progression alive.
Gers boss Giovanni van Bronckhorst told Premier Sports: "It was very disappointing. We have so much at stake in this month, qualifying for the Champions League, but the performance today was below par.
"At the beginning they dropped deep which means they were afraid but we didn't do anything with our ball possession and were sloppy, losing a lot of ball, not winning the duels, and slowly they became better and better.
"We didn't react well after that, we were never really in the game, we made many mistakes, giving a lot of transition moments away defensively and we were a little bit lucky that it was only 2-0 even though the penalty decision - I was surprised he gave a penalty.
"We have so much at stake with all the clubs involved in the competition, you want make the right decisions.
"We couldn't do anything else with the deflection, with the handball.
"The penalty was given, they scored and the most important thing now is to reflect on our own game because we need to change it around next Tuesday and we need to change it around big-time and the performance needs to be a lot better than we showed today."
He added: "We are still in the tie. A 2-0 difference. We are capable of making that up at Ibrox on Tuesday but first of all we need to concentrate on our performance and if we have the same performance then we have no chance next week."