Jamie Redknapp and Robbie Fowler each scored twice and Paul Ince also got a goal in a match that was so one-sided it threatened to become boring. Little went right for the hapless visitors, who appeared to have gone backwards even from their lacklustre performances against Manchester United last season.
The drama revolved around the second-half sending-off of Kosice's Marek Spilar, while the surprise was that Liverpool could score five goals without Michael Owen figuring.
Steve McManaman had been withdrawn on Monday and Fowler's latest game in pursuit of full fitness had also been heralded, so the only change that could be described as a surprise was the reintroduction of David James. Then again, after Brad Friedel's performance at Old Trafford it hardly registered on the Richter scale.
Frankly, Sid James could have been in the Liverpool goal because Kosice proved to be no threat. The home side could have been two up within five minutes - Redknapp and Fowler missing chances - and even then it was clear complacency could be their greatest opponent.
Not that Liverpool did not give that a good run for its money before taking the lead after 23 minutes. Never more so than when Fowler missed a penalty after Owen had been brought down by Spilar on the quarter hour. Fowler's kick was neither hard enough nor far enough away from Ladislav Molnar and he saved easily to his right.
Much more of this and even the Slovakian champions might have been encouraged but the goal that knotted the tie even more firmly duly arrived soon afterwards. Redknapp was tripped by Radoslav Kral 20 yards out but carried out his own retribution, drilling low into the corner after Paul Ince had passed through Patrik Berger's legs to him.
The first half finished with Berger hitting a post and Owen the bar, the latter a culmination of a fine move down the left involving Redknapp and Fowler, but if the interval marked a change in the game's mood it was only that Liverpool stopped regarding it as a pre-season friendly. Instead of missing at will, they became Robin Hood-like with their accuracy and three goals arrived between the 52nd and the 55th minutes.
Ince slid the ball in from three yards; Fowler headed in after the Kosice goalkeeper had made a hash of Stig Inge Bjornebye's cross; Redknapp lashed in from 30 yards; Liverpool have rarely had an easier night in Europe.
The more so after 59 minutes when the onslaught became too much for Spilar and his tackle on Owen led to his sending-off. Fowler added another goal a minute from the end but Spilar could console himself that the tie had disappeared down the tunnel a long time before he did.
"With the advantage we had from the first leg, we feared the players might take it easy," Gerard Houllier, Liverpool's joint manager, said, "but they performed in a very, very professional way."
Liverpool (4-4-2): James; McAteer (Heggem, 65), Carragher, Babb (Matteo, 62), Bjornebye; Leonhardsen, Ince (Staunton, 70), Redknapp, Berger; Owen, Fowler. Substitutes not used: Kvarme, Murphy, Thompson, Friedel (gk).
Kosice (3-5-2): Molnar; I Kozak, Semenik, Spilar; Sovic (Lapsansky, 61), Kral (Jambor, 56), Dzurik, J Kozak, Gerich; Nemeth (Kozlej, 61), Zvara. Substitutes not used: Skolnik, Prohaszka, Lubarskij, Seman (gk).
Referee: P Garibia (France).Reuse content