Summer signing Christian Manfredini provided the perfect riposte to any critics after Lazio's opening day Serie A defeat against his former club Chievo by putting his new side ahead on the stroke of half-time.
That handed the Biancoceleste the platform to build a commanding advantage for the trip to Greece in a fortnight's time.
Claudio Lopez added the second on 51 minutes and two in two minutes from Simone Inzaghi and Cesar midway through the second half ensured the return leg should be little more than a formality for Lazio.
Parma snatched a priceless away goal as they earned a 1-1 draw against CSKA Moscow in their first round Uefa Cup encounter.
The Italian outfit are now firm favourites to advance to the second round when they entertain the Russians at Ennio Tardini.
New signing Adrian Mutu continued his fine start to his Parma career as the Romanian fired the visitors ahead on 52 minutes but Denis Popov equalised for CSKA on 67.
Chievo Verona marked their baptism in European competition by grinding out a 0-0 draw at former European Cup winners Crvena Zvezda.
Uefa Cup First Round First Leg Results:
Crvena Zvezda 0-0 Chievo Verona
CSKA Moscow 1-1 Parma
Lazio 4-0 Xanthi
