Williams made all three of his shots in the second quarter, including a layup that gave the Nets a 62-49 lead at the break.
Phoenix cut it to 76-67 on Morris' three-point play, but Johnson and Paul Pierce hit consecutive 3-pointers to start a 14-0 burst and gave the Nets a 90-67 lead with 1:20 remaining in the third quarter.
Williams stopped one last Phoenix attempt to get close in the fourth, nailing a 3-pointer after the Suns had closed within 12.
NOTES: Brooklyn has won the last five meetings. ... New Jersey's Jorge Gutierrez played 7 scoreless minutes on the day he signed a second 10-day contract. He played in only one game during the first deal. ... The game featured two sets of brothers, with the Suns' Morris twins, Markieff and Marcus, and the Plumlees.