Will Barton made four straight free throws in the final 7.9 seconds for Denver (24-23), which had lost two in a row and six of its last eight outings.
Damian Lillard collected 25 points and eight assists and Jusuf Nurkic contributed 19 points and 12 rebounds for Portland (25-22), which saw the end of a three-game win streak.
Neither team led by double digits in a game that featured 18 lead changes and 21 ties.
Trailing by four points at halftime, Denver scored the first eight points of the third quarter to go ahead 53-49. The Blazers had a 78-76 edge heading into the final period.
The teams were tied at 80-80 when Portland went on a 13-6 run to go ahead 93-86.
Mason Plumlee's dunk got Denver to within 93-90 with 3:53 to play.
Nurkic scored on a layup to push Portland's lead to 95-90 with 3:39 left. Barton sank two at the line to cut it to 95-92 with 3:18 to go, and Murray's 3-pointer tied it at 95-95 with 2:07 remaining.
Plumlee's layup gave Denver a 97-95 led with 1:26 remaining. CJ McCollum hit two free throws to tie it at 97-97 with 1:08 left.
Lillard's runner pushed the Blazers back in front 99-97 with 41.7 seconds to go. Murray's three-point play pulled Denver ahead 100-99 with 33.6 seconds to play.
Barton's two foul shots with 7.9 seconds remaining upped the Nuggets' advantage to 102-99 with 7.9 seconds on the clock. Nurkic dunked with 2.6 seconds to go to trim the difference to 102-101, but Barton answered with a pair of free throws with 1.8 ticks left to ice the verdict.
Murray scored 11 points to help stake Denver to a 20-19 lead after one quarter.
Lillard scored 13 points in the second quarter as Portland carried a 49-45 advantage at intermission. The Nuggets had 10 turnovers in the first half.
--Field Level Media
Portland | Denver | |
Damian Lillard 25 | Scoring | Jamal Murray 38 |
Damian Lillard 8 | Assists | Jamal Murray 6 |
Jusuf Nurkic 12 | Rebounds | Nikola Jokic 12 |
CJ McCollum 6 | Free Throws Made | Will Barton 7 |
Pat Connaughton 3 | Steals | Wilson Chandler 2 |
Jusuf Nurkic 3 | Blocks | Wilson Chandler 3 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Portland | 101 | 42.4 | 8-25 | 21-26 | 19 | 44 | 6 | 11 | 12 |
Denver | 104 | 41.0 | 10-30 | 26-33 | 23 | 49 | 8 | 7 | 15 |