Rodrigo Bentancur's header ricocheted of Kean's head and into the back of the net after 16 minutes in the game's decisive moment.
But Jose Mourinho's side were furious when Tammy Abraham put the ball in the net but the goal was not allowed to stand because referee Daniel Osrsato had already whistled for a penalty.Jordan Veretout took it and his effort was saved by Wojciech Szczesny.
"I know it would be complicated.Roma certainly would have fully deserved a draw because they played a great match,"Juventus coach Massimiliano Allegri to DAZN.
"These games are decided by episodes and they went our way tonight fortunately, but also because when you play as a team with the right spirit, things go your way.
Juventus are seventh with 14 points, level with Lazio and Atalanta above them and one point behind fourth-placed Roma.
The result continues their recovery from a shock failure to win any of their opening four league matches.
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