Denver won its third in a row, getting a 30-point performance from Lawson and 29 more from Andre Iguodala.
After trailing narrowly for most of the fourth period, Denver went in front by two on a layup by Andre Miller with 24.9 seconds to play. Lawson's two foul shots at the 13-second mark gave Denver a 110-106 advantage.
Portland then gave itself a chance when Damian Lillard hit a 3-pointer, after which Miller could make just 1-of-2 from the line with 3 seconds to play.
That gave the Trail Blazers an opportunity to win it or force overtime, but LaMarcus Aldridge missed a shot at the buzzer from inside the 3-point arc.
Lillard led Portland with 26 points and Aldridge had 22. The Trail Blazers have lost eight of nine, failing to back up their victory over Boston Sunday.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut