French winger Dembele fired Barcelona ahead after 34 minutes at the Cotton Bowl, wriggling past Juventus players Juan Cuadrado and Sandro before beating Juve goalkeeper Wojciech Szczesny to make it 1-0.
But Juventus hit back five minutes later with Colombian wing-back Cuadrado making amends with a pinpoint low cross that found Kean who tapped in past Barcelona goalkeeper Marc-Andre ter Stegen.
Barcelona were soon back in front again, however, and once again the goal came as Dembele punished poor defending.
Cuadrado was again at fault, with Dembele skipping past the South American’s covering tackle and then cutting past Manuel Locatelli to shoot past Szczesny for a 2-1 lead.
Barcelona coach Xavi Hernandez made a flurry of changes at half-time, with Dembele making way for new Brazilian signing Raphina.
The former Leeds striker made an instant impact, blasting a long-range shot that Szczesny parried over the bar.
Despite Barcelona’s bright start to the half, it was Juventus who scored next with Kean tucking away a rebound after deft approach play by Denis Zakaria and Locatelli on 52 minutes.
Barcelona came closest to the breakthrough goal, and hit the woodwork twice in a matter of seconds on 68 minutes.
Raphina rattled the crossbar with a curling free kick and from the rebound Ansu Fati’s curling shot from the edge of the area cannoned back off the post.
That was as close as either side came to breaking the deadlock, while Barcelona’s new signing Robert Lewandowski struggled to make much of an impression before being substituted midway through the second half.