Carolyn Swords had 12 points, three steals and a career-high five blocked shots for New York (4-3), which had dropped two in a row. Sugar Rodgers scored 17 points, and Tina Charles added 13 points and 12 rebounds.
The Liberty closed the first quarter with a 14-2 run to take a 21-10 lead and never trailed again. New York led by as many as 21 in the third quarter.
Sancho Lyttle made a 3-pointer and a jumper to close a 10-0 run by Atlanta (3-5), trimming its deficit to 63-56 with 1:59 to play, but Boyd and Rodgers combined to go 10 for 10 from the free-throw line down the stretch for New York.
Angel McCoughtry led the Dream, who shot a season-low 29.7 percent (19 of 64) from the field, with 17 points. Roneeka Hodges added 12 points, and Lyttle finished with 11 points and six steals.
New York, which improved to 20-10 against the Dream, outscored Atlanta 36-14 in the paint.