Dembele opened the scoring in the 34th minute with a fine solo effort, dribbling past Juan Cuadrado (34) and Alex Sandro (31) before drilling a fierce shot past goalkeeper Wojciech Szczesny (32), but his goal was cancelled out by Moise Kean's (22) equaliser in the 39th minute.
Dembele immediately restored Barcelona's lead, scoring his second just a minute later, only for Kean to once again draw Juventus level with a second-half strike.
Speaking after the match, Xavi lavished praise on Dembele, who has struggled to make an impact since joining Barcelona in 2017, saying he has shown a marked improvement in the eight months since Xavi took charge in November last year.
"He has shown what he is capable of. He is different, special. There are not many of this type," Xavi told reporters on Tuesday.
"He gives us a lot with the way we play.
"Not everyone has the ability to make a difference in the world of soccer and he does. He is involved and he shows it. I don't know the Dembele from before November, I don't know him. I am very happy with this one."
Barcelona, who finished second in La Liga last season, kick off their league campaign at home to Rayo Vallecano on August 13.
