In sweltering conditions of 40 degrees Celsius in the northern province of Kumanovo, Portadown managed to shut out the home side, which features several Macedonia internationals.
Keeper David Miskelly was the star of the show, making a string of saves to keep the hosts out.
There had been some controversy in the build-up to the clash, as Portadown were only given a week to prepare for the conditions and a journey they could barely afford.
The return leg takes place on Tuesday July 10 at Shamrock Park.
In the other Europa League first-round qualifying first leg on Tuesday, Gomel won 6-0 at Vikingur in a meeting of the teams who finished third in Belarus and Faroe Islands respectively.
A further 35 ties are to be played on Thursday.