The former Manchester United captain glanced in a header from a free-kick late in the first half before Yuto Nagatomo added a second after the break.
After Inter's second win in the International Champions Cup, Mazzarri stated his delight at his side's showing and, in particular, the performance of Vidic.
"I'm really happy with the lads, we're getting better by the game. Solid in defence, Vidic is top class," the coach told Inter Channel.
"We're creating lots in the final third, we just need to be a bit sharper with our final ball.
"We must keep going like this."
The victory keeps Inter in with a chance of remaining in the competition but, if they bow out, a friendly with Eintracht Frankfurt awaits.