Traianos Dellas sent the hosts on their way with the opener on 12 minutes and Daniele De Rossi added a second seven minutes later.
Norwegian striker John Carew grabbed his second goal for the club on 53 minutes and Marco Delvecchio added a fourth in stoppage time to make the second leg in Macedonia little more than a formality.
Dundee face an uphill battle to keep their Uefa Cup dreams alive after going down 2-1 to Perugia in the first leg of their Uefa Cup tie at Dens Park.
Massimiliano Fusani's late goal was enough to give the Serie A side a crucial first leg advantage after Nacho Novo had cancelled out Marco Di Loreto's opener for the visitors.
Perugia dominated the first half, but could not find a way past the impressive Julian Speroni in the Dundee goal.
The Italians finally broke the deadlock on 52 minutes with Di Loreto sending a looping shot over the despairing Speroni.
Dundee fought back and drew level with Novo claiming he got the last touch on Lee Wilkie's header to divert the ball into the net.
The game looked set to end all-square until Fusani popped up seven minutes from time to curl a fantastic shot from the edge of the box after Dundee failed to clear their lines.
Adriano saved Parma from a surprise defeat to Ukrainian side Metalurh Donetsk after a 1-1 draw in the first leg of their first round Uefa Cup tie.
Serhiy Shyshchenko fired the hosts in front on the stroke of half-time as they threatened a major surprise.
Parma fought back and grabbed a crucial away goal on 67 minutes through Brazilian hit-man Adriano and they will be firm favourites to finish the job off at the Ennio Tardini.
Udinese are in the driving seat in their tie with SV Salzburg after an impressive 1-0 in Austria.
Dino Fava grabbed the all-important winning goal for the Italian side after 36 minutes to put them in pole position for the second leg.
