Mauro Camoranesi, Giorgio Chiellini, Nicola Legrottaglie and an Alex Del Piero screamer virtually settled the tie in Juve's favour.
"This result is important, but we have to go there concentrated, as this team beat Celtic 5-0. We need to remember that," said Juve coach Claudio Ranieri.
"It was crucial to score goals on our return to the Champions League and the lads played a great game."
Del Piero opened the scoring with a stunning strike remarkable for its power and precision, but also inspired his teammates with some great touches.
"Alessandro is going through a wonderful period of form. He was unable to do the pre-season training he wanted last term and suffered because of that situation, but he is in great shape and everyone can see that," continued Ranieri.
"I think each half is a game in and of itself, so really this tie is four matches and we are only midway through. The result has to be earned in Slovakia."