Mancini struck early in the second half of Sunday's match to help Roma move into fourth place in Serie A in a tight fight for the Champions League qualifying spots.
There was further misery for Juventus as substitute Moise Kean was sent off in the final minute, seconds after coming off the bench, for violent conduct.
Roma is above fifth-placed AC Milan on goal difference alone after the defending champions lost at Fiorentina on Saturday.
Juventus are 12 points further back, having had 15 points deducted at the start of the year for false accounting.
Roma coach José Mourinho was on the bench during the match against Juventus after his two-match ban was suspended.
Mourinho was banned after being sent off in Roma's surprise loss to Cremonese but an appeal court suspended the decision until after hearing from the fourth official.
The game sprang into action moments from halftime as Roma goalkeeper Rui Patrício pulled off a great save to turn Adrien Rabiot's header onto the post.
However, it was Roma who took the lead eight minutes after the break when Mancini hit a rocket from 25 yards out into the bottom left corner.
Juventus almost equalised immediately but Juan Cuadrado's free kick clipped the post.
The visitors had a third chance hit the woodwork late on with Mancini almost going from hero to villain after his defensive header from a Juventus corner came off the left post.
Kean was shown a straight red card after he reacted angrily to being held back by Mancini, kicking the Roma defender in the back of the leg.
AAP
