The Clippers recorded 10 consecutive misses in the third quarter, allowing Denver to cut the points gap and take control to win 111-98, BBC Sport reported.
Nikola Jokic scored 34 points to help force a series decider on Tuesday.
"We don't have pressure," Jokic said. "All the pressure is on them. To us it's just another game seven."
The Nuggets needed seven games to beat the Utah Jazz after trailing their series 3-1 in the last round and have now become the first team since the 1970 Los Angeles Lakers to force multiple deciders in the same NBA Playoffs run.
If they win on Tuesday to set up a Western Conference Final against the Lakers, Denver would become the first side to recover from 3-1 down twice in the same playoffs.
The Clippers are aiming to reach a first conference final in their 50-year history.
Speaking after the defeat at Disney World in Orlando – where games are taking place in the coronavirus quarantine bubble – Clippers star Kawhi Leonard said his team "couldn't buy a basket" during the Nuggets' comeback.
"It was beautiful," said Clippers coach Doc Rivers. "Then we stopped moving the ball, stopped playing. That's what let them get back in the game.
"We clearly have the right formula. We just lost it. We lost our pace."