Dembele opened the scoring with a brilliant individual effort just after the half-hour mark at the Cotton Bowl, but Kean replied for Juve soon after.
A second Dembele strike -- off another fine solo run -- handed Barca the lead at the break only for Kean top level for Juventus again early in the second half.
Instead the plaudits here went to Dembele, who scored two stunning goals at the end of the first half.
Kean turned home a Cuadrado cross five minutes later to level the game, but Dembele wove his way through the Juve defence again just before the break to restore Barca's lead.
Both teams made wholesale changes at half-time, with Frenkie de Jong coming on as a central defender for Barca for the third successive friendly, but it was Kean who was once again in target in the 51st minute.
Both sides continued to make substitutes, disrupting the flow of what had been an entertaining game, but it was Barca who came closest to winning the match.