Dybala hit two goals in the first half to give the Italians a comfortable lead heading into next week’s quarter-final second leg at the Nou Camp.
But the Argentina is mindful of Barcelona’s ability to bounce back from the dead after their stunning turn-around against Paris St Germain in the last eight.
Dybala said: “We played a great game and we made the best of the chances we had and it is certainly a great result ahead of the return leg in Barcelona.
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Juventus players celebrate with fans after huge win over Barcelona
“We are in a very good position and we’re playing with great confidence, but we cannot relax because it will be very difficult at the Camp Nou.”
Juventus coach Massimiliano Allegri echoed Dybala’s cautious sentiments but was plainly delighted with a performance which was capped with a rare second-half goal from Giorgio Chiellini.
Allegri said: “I must congratulate my players, but there is another match to play. I think this is an important step forward in our objective to reach the final.”
Defiant Barcelona star Andres Iniesta insists it is still all to play for in Barcelona next week – and it is less of a challenge than that faced against PSG in the last round.
Then, Barcelona managed to overturn an even greater deficit as they recovered from a 4-0 mauling in the French capital to win 6-5 on aggregate.
Iniesta insisted: “We will turn the tie around if we do things as we need to do in Barcelona.
“Juve are a good team, but when you don’t do things well you get punished. However, we don’t feel as bad as we did in Paris, but we have another big mountain to climb.”