Lopez supplied 22 points and 11 rebounds while Williams contributed 16 points and 14 assists as Brooklyn improved to 7-1 at the newly-opened Barclays Center.
The Knicks were initially scheduled to face the Nets in their first game after moving to Brooklyn during the off-season, but that Nov. 1 contest was postponed due to flooding caused by Hurricane Sandy.
After New York rallied from a late five-point deficit to force overtime, Brooklyn locked up its third straight win with a 7-0 run in the extra frame.
Carmelo Anthony pumped in 35 points and hauled down 13 rebounds, but it wasn't enough for the Knicks, who managed to hit just 25.8 percent of their field goal tries after the third quarter.
Tyson Chandler provided a career-high 28 points and 10 rebounds for New York.