The hosts twice went close to falling behind inside the opening half hour.
Juventus were punished for their poor finishing on 31 minutes, as Oscar's 25-yard effort deflected past Gianluigi Buffon into the top corner of the Italians' goal.
If his first strike was a little fortunate, his second - two minutes later - was of the highest quality.
Ashley Cole found the Brazilian on the edge of the penalty area and, following a sublime first touch that spun him away from Andrea Pirlo, he hit a stunning first-time effort, which curled into the top corner.
Vidal reduced the Blues' advantage seven minutes before the break with a low left-footed drive from 20 yards.