While the Rossoneri sweat over their chances of competing in next season's Champions League, Juve can seal a second straight Scudetto by winning next Sunday's derby meeting with Torino, should second-placed Napoli fail to beat Pescara.
A Vidal penalty in the second half was the difference between the two sides, who are now separated by 18 points with five games remaining.
The result means the Bianconeri are assured of their place in the Champions League next season while, with an 11-point cushion over Napoli, they could wrap up the title with four games to spare.
Milan, however, are looking over their shoulders with fourth-placed Fiorentina now just a point behind in the race for Champions League football.
Rossoneri head coach Massimiliano Allegri picked an attacking line-up in response to Napoli's earlier 3-2 win over Cagliari which opened a seven-point gap between second and third place.
Robinho, one of three forwards in his starting XI, tried his luck in the early exchanges but just missed the target.
Andrea Pirlo went closer to breaking the deadlock in the eighth minute with a free-kick that took a deflection off Massimo Ambrosini in the wall, making life difficult for Christian Abbiati who somehow managed to change direction and turn the ball behind for a corner.
Milan's top goalscorer Stephan El Shaarawy responded by giving Gianluigi Buffon his first test of the evening in the 24th minute.
Marco Amelia soon came on for the injured Abbiati and he had to deal with another deflected Pirlo free-kick as the two sides reached the break on even terms.
The substitute keeper negatively affected his team, however, as his foul on Kwadwo Asamoah in the 57th minute earned Juve a penalty.
Chile international Vidal made no mistake when placing his spot-kick high into the net to give the hosts the lead.
Milan responded brightly with Sulley Muntari and Riccardo Montolivo both testing Buffon.
But the visitors just could not find an equaliser, despite introducing a fourth striker in the shape of Bojan Krkic, and Juve rode out the final throes to edge closer to their 29th domestic title.