Lou Williams scored 18 points and Jason Kapono had 14 for Philadelphia, which rebounded from a 31-point loss to Boston three days earlier.
Brook Lopez led the Nets with 22 points and 11 rebounds while Trenton Hassell had 17 points and 12 rebounds. New Jersey fell to 0-6, the worst start in franchise history.
The Nets were without six players due to injury and had only a four-man bench.
After Lopez tied the game at 92 with a pair of free throws, Iguodala made a 3-pointer to put the 76ers up with 2:03 left.
New Jersey lost guard Courtney Lee early in the third quarter with an apparent leg injury. The Nets were already missing guards Keyon Dooling (hip surgery), Chris Douglas-Roberts (flu), and Devin Harris (strained right groin); as well as forwards Tony Battie (right knee), Yi Jianlian (sprained right knee) and Jarvis Hayes (strained left hamstring).
New Jersey built a 73-65 lead with 1:51 left in the third quarter and carried it into the fourth quarter.
Terrence Williams's short jumper made it 87-81 with 7:54 remaining, but the Sixers came back with an 11-3 run to take a 92-90 lead with 2:54 left.
Lopez then hit a pair of free throws to tie the game before Iguodala's 3 and the 76ers struggled briefly from the line to close out the Nets.
Rafer Alston made it 95-94 on a driving layup with 50.3 seconds left and Thaddeus Young made one of two free throws for Philadelphia with 21.8 seconds left.
Eduardo Najera missed a seven-foot bank shot in traffic and Iguodala hauled in the rebound for the Sixers. After being fouled, he also made one of two, but kept the Nets from attempting to tie the game when he deflected the ball from Williams' hand.
NOTES: Sixers coach Eddie Jordan was an assistant under Nets coach Lawrence Frank when they reached the NBA Finals in 2002 and 03. ... In 1996-97, the Nets began 0-5 and won a game before finishing 26-56. ... Hassell hadn't scored in eight minutes all season before his double-double against the Sixers. ... The game had 22 lead changes and 17 ties. ... Marreese Speights added 10 points for the Sixers.