The Blue Devils (9-2) poked and prodded UCLA's 2-3 zone from the perimeter, making 11 3-pointers in a season-high 32 attempts from beyond the arc. Parker went 4 for 8 from long range while going over 20 points for the ninth time in his 11 college games.
Rodney Hood and Quinn Cook both had 14 points for the Blue Devils.
UCLA's zone kept the Bruins in the game. Wear's 3-pointer, one of his four for the game in as many attempts, tied it at 43 with 17:58 to play.
Duke suddenly began to connect from outside with consistency and Hood hit two 3s and Parker added another in a 16-4 run that put the Blue Devils up 61-49 with 11:33 to go.
The Bruins twice got within eight points, but they got no closer in front of the crowd of 15,410.
UCLA, which entered the game averaging 85.1 points, was 8 of 22 from 3-point range. Jordan Adams, the Bruins' leading scorer coming in with a 21.2 average, was held to 10 points on 4-of-10 shooting.
The win was Duke's 23rd straight in the month of December and lifted Blue Devils coach Mike Krzyzewski to an 8-1 record against UCLA.
The Blue Devils are 2-1 at Madison Square Garden this season having beaten Alabama and lost to Arizona in the NIT Season Tip-Off in November. Duke's other loss this season was to Kansas.
UCLA's other loss this season came at Missouri on Dec. 7.