"You always need wins to believe," Cleveland coach Mike Brown said. "Winning for the most part is the thing that cures everything. In the same breath, (this is) a learning process. It's not going to happen overnight."
The Cavaliers (6-12) won back-to-back games for the first time this season, and they snapped the Nuggets' seven-game winning streak.
Thompson said he wasn't thinking about posting his first career 20-point, 20-rebound game.
"I wanted to play within the offense," Thompson said. "If it happens, it happens. I'm not going out searching for it."
His teammates, however, wanted him to attain the feat.
"He almost had a 20-20 game, and I was fighting Coach Brown to call his number," Cavs point guard Kyrie Irving said. "That's what we need from him every single night."
"To get 34 rebounds between two guys is an amazing night for our bigs," Brown said. "They were monsters on the glass. They were monsters around the rim. It was awesome to watch."
The Cavs hammered Denver on the boards, 58-43, including a 20-15 edge on the offensive glass. The Nuggets came into the game one of the top rebounding teams in the NBA.
"If I wasn't going to get the rebound, he wasn't going to get it either," Thompson said. "He brings that kind of spark to their team. He kind of gets them going, so my role is just to take him out tonight, and that's what I did."
The point guard duel was another mismatch, as Irving outscored Ty Lawson, 23-4.
Lawson finished 1-for-13 from the field.
"I just feel like I missed all these shots," the former North Carolina standout said. "In and out, in and out. I never shot 1-for-13 in my life."
Conversely, Irving was 9-for-20 from the field and 2-for-5 from the 3-point arc.
"I wanted to make it difficult for (Lawson)," Irving said. "I was always the first one back (on defense)."
"While we're going through all this, we're learning how to win," Brown said. "We're trying to figure ourselves out."
NOTES: Nuggets coach Brian Shaw said he interviewed for 12 head-coaching jobs in the NBA before he was hired by Denver. He interviewed with the Cavaliers in the summer of 2010 just after they fired Mike Brown. At one point during the process, Jerome Stanley, Shaw's agent, tweeted that his client received the job -- a fact that was disputed by the team. The Cavaliers instead hired Byron Scott, who compiled a 64-166 record, their worst record ever during a three-year span. ... Brown, in his second stint as CLEVELAND's coach, said he wants to keep C Andrew Bynum's minutes around 25-28 per game. Bynum played a season-high 30 against the Chicago Bulls on Saturday. ... Cavaliers G Dion Waiters recorded three consecutive 20-point performances off the bench heading into Wednesday's game. Only one other NBA player accomplished that this year: Suns F Markieff Morris from Nov. 6-10. The Nuggets limited Waiters to five points. ... Brown said he expects Nuggets F/C J.J. Hickson to behave himself. "I'm sure if he gets out of line, his grandma will come and grab him by the ear," the coach joked.