Jrue Holiday finished with 22 points, Elton Brand notched a double-double with 16 points and 17 rebounds. Meeks ended with 17 points for the Sixers, who snapped a two-game skid and are now 2-2 on a eight-game road trip.
"Once again our defense gave us a chance," Philadelphia coach Doug Collins said. "We won this game today shooting under 40 percent from the floor, 3-of-14 from three, missing 12 free throws."
Chauncey Billups finished with a game-high 24 points, Arron Afflalo and Ty Lawson both scored 14 and Nene had 13 points and nine rebounds for Denver, which was without superstar Carmelo Anthony. He missed his third game in a row following the death of his sister, Michelle Anthony, who passed away due to a pre-existing medical condition.
The Sixers were without guard Lou Williams who is home expecting the birth of his daughter. Williams will also miss Monday's game at Golden State.
The Nuggets were up 82-70 after two Billups free throws with 8:11 remaining, but a Brand layup on the Sixers' next possession started a 19-2 run that gave the Sixers the lead in the final minutes.
"I think it's something we have to spend some time watching on film, going through game-type situations in practice," Billups said of the fourth-quarter meltdown.
After his layup Brand added a putback shot just inside seven minutes to put the game at 82-74. Meeks connected on four free throws and Iguodala hit a short jumper with 5:08 remaining to put the game at 82-80.
After Holiday tied the game at the line, Billups hit on two from the charity stripe with 4:18 left to keep the Nuggets advantage at 84-82. Thaddeus Young then added two of his 20 points off the bench with a short jumper on the next possession, and Iguodala made the front end on two from the line to give the Sixers an 85-84 lead with 3 1/2 minutes remaining.
A Holiday jumper and two Brand free throws extended the Sixers' lead to five to cap the run and give Philadelphia a 89-84 advantage.
Nene ended the run when he hit on a convincing dunk just over the minute mark, but Meeks hit his long three to put the Sixers up six, 92-86, to seal the victory.
The Nuggets were forced to foul down the stretch and the only shot they made was a Billups three with 17.8 seconds left, but Philadelphia was already up eight at that point.
Denver took a 25-13 lead after the first, but shot 35 percent from the field in the second, and Philadelphia cut the margin to 46-43 at the half.
Holiday led the Sixers will 11 points in the third, but Denver outscored them 25-23, en route to a 71-66 lead entering the fourth.
The Nuggets have lost three straight...Denver shot 91.3 percent from the foul line...Philadelphia is now 4-12 on the road, and will finish off its trip with visits to Golden State, Phoenix, the LA Lakers and New Orleans...Philadelphia was also without assistant coach Brian James due to a death in the family.