All five Nuggets starters scored in double digits, with Kenneth Faried supplying 18 points and 16 rebounds and Ty Lawson adding 19 points, including eight during a game-ending 14-2 run.
The Clippers were trying to become the first team this season to win 12 in a row, but they were outscored in the paint by a 54-44 margin and made just five of their 21 3-point attempts.
There were 13 lead changes and 14 ties over the first three quarters, and it was even at 83-83 entering the fourth.
Neither team led by more than five from there until the Nuggets pulled away in the final 4 1/2 minutes. Lawson started the surge with a go-ahead 3-pointer, added a three-point play the next time down, and by the time Randy Foye hit from long range, Denver suddenly had a 107-100 lead with 2:35 to play.
The Clippers, who were coming off a 22-point home win over the Cavaliers on Sunday, faded away in crunch time, missing seven of their last eight shots to come up short.
Los Angeles held a slim 25-23 lead after one quarter, and despite Paul's 14 points in the second, Denver took a 56-53 edge into halftime.