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Vidal just managed to beat Nicola Leali from 12 yards to give the Bianconeri the lead, but the midfielder could have opened the scoring in the first two minutes as he blazed a half-volley over the Cesena crossbar.
Juventus dominated possession for much of the first half and had chances to increase their advantage.
Fernando Llorente squandered a good opportunity when Patrice Evra's cross reached the Spaniard, but his effort from eight yards out was wayward.
With half time approaching, Giovinco also went close for the champions when his fierce drive from distance flew narrowly wide of Leali's goal.
Midway through the second half, Juve gave themselves a two-goal lead when Llorente made amends for his earlier miss by flicking the ball into the path of Vidal and, from 20 yards, he found the bottom corner of the net.
Allegri's men almost piled further misery on Cesena in the 75th minute as new signing Alvaro Morata looked to shoot on the turn, but knocked the ball away with his standing foot at the crucial moment.