Gais dominated much of the first half, but it was not until the final minutes of the half that the breakthrough came. A fine Gais move ended with a cross from August Wängberg that found Matteo de Brienne, who volleyed in the opener.
"It's a dream, it feels good to do it for the people here," the scorer said after giving his team the lead in Sportbladet's broadcast.
In the second half, Nordsjælland took over and the home side largely had to defend for the final 45 minutes.
The Danes created chance after chance, but Gais held on and now have a dream position to advance to the next qualifying round.
The return match against Nordsjælland will be played on July 30.
