Brooklyn led by 20 after the opening period and was not threatened while remaining within 2 1/2 games of New York for the lead in the Atlantic Division.
Lopez scored 28 points and Evans came through with 22 points and a career-best 26 rebounds. Brooklyn outrebounded Portland by 14.
LaMarcus Aldridge had 24 points for the Trail Blazers, who fell for the second straight game and are now 3 ½ games behind the Los Angeles Lakers for the eighth and final playoff spot in the Western Conference.
Brooklyn is 4-1 on an eight-game road trip that lasts through April 3.