Last season Kosice lost both their Champions' League ties to Manchester United by 3-0 scorelines, and they suffered the same humbling in front of their own supporters here.
Patrik Berger, Liverpool's Czech forward, opened the scoring with a stunning 30-yard drive in the first half and turned in an outstanding display. His team-mate, Karlheinz Riedle, added another soon afterwards and in the second half Fowler stepped from the bench to make a superb third for Michael Owen with his first touch of the ball.
Liverpool displayed all their flowing attacking skills at the Locomotiva stadium, even if the defence at times looked less than convincing. But the Merseyside club will not want to dwell on those occasional shortcomings. They were far too good for the Slovakian champions.
Without their injured captain, Paul Ince, Liverpool had Steve Harkness in midfield, while Steve McManaman led the side. Fowler was named for a senior game as a substitute for the first time since he damaged cruciate ligaments in February.
Owen found himself a marked man, with Kosice defenders taking it in turns to foul him from behind almost at will. However, it was this level of intimidation from the Slovaks that earned Liverpool their first goal. It came after 18 minutes, when Marek Spilar clattered Owen 30 yards out from Steve Staunton's tapped free-kick. Jamie Redknapp stepped over the ball and Berger unleashed a searing low shot that crashed in off the inside of a post.
The Slovaks made a brief response but were stunned again five minutes later when Liverpool scored their second goal. McManaman got away from Dusan Toth on the right and fired over a fine cross that was met in the six-yard box by the unmarked Riedle, who powered a header past the helpless Ladislav Molnar.
Owen, who was still receiving treatment when Riedle's goal went in, was once again left in a painful heap by Ivan Kozak, who somehow avoided a yellow card.
Liverpool maintained their grip in the second half, with Fowler finally getting his first taste of action when he came on as a 58th-minute substitute for Riedle. Within 26 seconds of his arrival and with his first touch, Fowler created a goal for Owen, threading a perfect through ball. Owen took his revenge on the Slovak defenders by racing away and gliding a sidefoot shot past Molnar.
Brad Friedel, Liverpool's goalkeeper, made a superb 65th-minute save from Peter Zurik's 20-yard power driver and handled a succession of high crosses with great calm. However, Liverpool finished in command and the second leg in a fortnight should be a formality.
Kosice: Molnar; Toth (Prohaszka, 67), I Kozak, Dzurik, Spilar, Sovic, Nemeth, Kozlej (Lubarskij, 67), Semenik, Zvara, Kral (J Kozak, h-t). Substitutes not used: Seman, Gerich, Lapsansky, Jambor.
Liverpool: Friedel; Staunton, Babb, McManaman (McAteer, 78), Owen, Redknapp (Leonhardsen, 83), Harkness, Riedle (Fowler, 58), Heggem, Berger, Carragher. Substitutes not used: James (gk), Kvarme, Bjornebye, Matteo.
Referee: J Arcio (Spain).