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.