Denver took a 10-point lead into the final period, but the Thunder went on a nine-point run early in the stanza to get back in the game and eventually went in front by three.
Denver let the clock run down before Lawson produced the last of his 11 points to win it.
Oklahoma City had won its previous three games while Denver ran its winning streak to four. The Nuggets are 25-3 at home this season, tops in the Western Conference.
Russell Westbrook had 38 points for the Thunder while Durant scored 25 and grabbed 14 rebounds.
Dennis Rodman pledges to end trips to North Korea
Susan Sarandon 'very excited' about daughter's pregnancy