"That's the good thing about being in the East right now and I'm sure every other team feels the same, but we truly believe we haven't played our best basketball," Brown said. "Contrary to what anybody believes I do feel like we're getting better."
Nate Robinson scored 14 points and Wilson Chandler added 13 for the Nuggets.
Denver got off to a slow start playing its third game in four nights. The Cavaliers led by seven points on several occasions in the first quarter and stretched the lead to 12 in the second. Cleveland led 54-42 with 1:51 remaining in the second, but Denver scored 10 of the half's final 12 points, highlighted by Lawson's three-point play, a 3-pointer by Foye and four points by Darrell Arthur.
Lawson's basket accounted for his first points of the game. He came into Wednesday averaging a team-high 20.2 points, but finished with four points on 1-of-13 shooting.
"I feel like I missed all easy shots," said Lawson, who had 11 assists. "I ain't never shot 1 for 13 before in my life."
Bynum was given a flagrant foul for hitting Hickson in the shoulder in the third quarter while the Denver forward was driving to the basket.
The Nuggets had won six of the previous seven meetings with the Cavaliers and three straight on the road.
Denver reserve center Timofey Mozgov had eight points and three rebounds in 17 minutes one night after grabbing a career-high 20 rebounds to go with 17 points against the Nets. He totaled 33 points and 35 rebounds against Brooklyn and Toronto.
NOTES: Robinson played despite re-injuring his right wrist Tuesday. X-rays after the game were negative. Robinson shot a free throw left-handed against the Nets. ... Robinson was given a technical in the second quarter after a foul wasn't called when he was knocked to the floor while taking a shot. ... Nuggets G Andre Miller was hit with a technical in the third quarter. ... Cleveland G Dion Waiters, who had scored at least 20 points in each of his last three games, had five points and six assists. ... Denver's road trip continues against Boston on Friday.