Williams finished with 26 points and 10 assists.
Johnson added 25 points, including nine during the big frame when the Nets outscored the Cavaliers 35-12.
Lopez helped out with 23 points as the Nets cruised to their third straight win and improved to 3-1 at their new Barclays Center home.
Cleveland, meanwhile, dropped its fourth consecutive game despite 35 points and 18 rebounds from Anderson Varejao.
Kyrie Irving also had a big night for the Cavs, firing in a career-high 34 points to go with eight assists.