Green went 10-for-12 from the field, 4-for-5 from 3-point range, in only 20 minutes.
Kevin Martin led the Kings (1-5) with 26 points.
Dallas was in front by as many as 12 early in the third quarter, but Sacramento used a 17-7 run to pull within 76-74 on Beno Udrih's three-point play.
The Mavericks built their lead back to 92-86 heading into the final quarter on Howard's buzzer-beating layup.
Green connected on a pair of 3-pointers in the first 2 1/2 minutes of the final quarter and Dallas went on to lead by as many as 26.
Green's 16 first-half points, including a spectacular double-clutch dunk in the second quarter, helped Dallas to a 63-54 halftime advantage. Martin had 20 first-half points and 8-of-14 shooting.