The Nets managed to see out the win as their defense shut out the opposition, while Paul Pierce also scored nine fourth-quarter points to push Brooklyn over the line.
"Stats just told us a stat where we are 13-0 when we hold teams under 40%," Williams told reporters after the game.
"So anytime you do that you give yourself a chance to win because we didn't shoot the ball well from three tonight, but we made up for it with effort, taking care of the ball, good defense down the stretch and making plays offensively. That is why we got the win."
The Nets now hold a 1-0 lead in their Eastern Conference first-round series.