The 22-year-old Canadian Murray combined with Serbian Nikola Jokic to form a dynamic scoring duo as the Nuggets squared their second round Western Conference series at two games each.
It was a quick turnaround from the Trail Blazers' 140-137 quadruple overtime victory in Friday's game three.
Game four didn't last nearly as long as that three hour, 35 minute marathon, but it was another back-and-forth battle highlighted by Murray's precision shooting and a fourth playoff triple-double from Jokic.
"The biggest part was mental," said Murray on playing two playoff games just 40 hours apart. "We know what to do physically but that was a draining game and we had to come back with energy and face a great team.
"We were able to get what we wanted on offence and the stops on defense."
Jokic had 21 points, 12 rebounds and 11 assists for his second straight triple-double and Murray, who led all scorers, was a perfect 11-for-11 from the free throw line for Denver, who handed Portland their first playoff loss at home this season.
Two free throws by Murray increased the Nuggets' edge to 112-108 with 13 seconds on the clock.
After Damian Lillard scored on a layup with 7.7 seconds remaining, Murray hit a pair of free throws to make it 114-110 with 6.7 seconds to play.
CJ McCollum scored on a long two-point shot to cut it to 114-112 with 4.4 seconds to go, but Murray clinched it with another pair at the line with 3.4 seconds left.
"I love free throws," said Murray, the son of Jamaican immigrants who moved to Kitchener, Ontario where he was born. "Everybody knows I love free throws. My team trusts me."
Said Nuggets coach Mike Malone, "Jamal has got a tremendous amount of grit. You think about how young we are and going on the road to win a tough game four in a hostile environment. For Jamal to be a centrepiece of that is phenomenal."
McCollum had 29 points and Lillard added 28 for the Trail Blazers.
Game five is Tuesday at Denver.
Elsewhere, Kawhi Leonard scored 39 points and pulled down 14 rebounds to propel the Toronto Raptors to a 101-96 victory over the Philadelphia 76ers that knotted their Eastern Conference series at two games apiece.
Spanish center Marc Gasol added 16 points and Kyle Lowry contributed 14 for the Raptors, who held ailing Sixers center Joel Embiid to 11 points on two-of-seven shooting from the field.
The Raptors will try to seize a series lead when the action shifts back to Toronto for game five on Tuesday.
After losing back-to-back games, Leonard said the Raptors' mindset was to "come in and play hard".
"The whole team concept was coming in and playing harder, being smarter and take your shots," Leonard said. "We needed it. This is a big win, but we've got to come back and get it for game five."
Leonard scored 17 points and grabbed 10 rebounds in a first half that finished with the Raptors holding a narrow 47-45 lead.
It was the first time in his career that he notched at least 15 points and 10 rebounds in a half.
After seven lead changes in the third quarter, the increasingly physical encounter was tied 75-75 heading into the fourth.
The Raptors were clinging to a 91-90 lead when Leonard drained a step-back three-pointer over a reaching Embiid with 1:01 left to play and three seconds left on the shot clock.
It put Toronto up 94-90 and the 76ers wouldn't get the gap below four points from there.
"I just saw there were about three seconds left on the clock," Leonard said of the clutch basket. "(Embiid's) so long so I just I just tried to fade away and shoot it over the top of him and luckily it went down."
The 76ers made connected on just five of 21 attempts from the field in the fourth quarter, missing nine straight in one span, and the Raptors made seven free throws down the stretch to seal it.