Six-time winners CSKA Moscow also kept their unbeaten record intact with a 95-82 home win over Lithuanians Zhalgiris Kaunas, thanks to centre Nenad Krstic, who scored 21 points, and fellow Serbian playmaker Milos Teodosic who had 14 and seven assists.
Navarro, who is in his 11th Euroleague season, received a standing ovation in the Blaugrana Arena when he achieved his target of 2,716 career points midway through the third quarter in Barcelona's 72-46 home rout of Slovenians Olimpija Ljubljana.
The versatile guard, who played in the NBA for the Memphis Grizzlies in the 2007-08 season before returning to his native Spain and Barcelona, finished the game on 14 points to beat the record held by former US shooting guard Marcus Brown.
"Navarro has this scoring record and he is a generous player who passes the ball as soon as he touches it," Barcelona coach Xavier Pascual told the competition's official website.
"What is more, he takes very little time to get a shot off so what he has accomplished has great merit.
"We are happy to have got this far undefeated, that was our objective at the start and we are delighted to have six straight wins but there is a lot left."
Barcelona are the 2010 winners of Europe's premier basketball club competition.
While most other top contenders are dreading the possible return of their NBA imports to North America, the depth of CSKA's squad made the absence of Utah Jazz starter Kirilenko and towering centre Darjus Lavrinovic barely noticeable.
Still, their Lithuanian coach Jonas Kazlauskas highlighted the duo's importance after seeing CSKA stroll to victory against his former club.
"We missed Kirilenko and Lavrinovic who played key roles in our first meeting with Kaunas," said Kazlauskas, who won five Lithuanian league titles with Zhalgiris in the 1990s and one with Lietuvos Rytas in 2002.
"Now I am trying to limit myself in my expectations and I am probably asking too much of my team because we can't win every game by a margin of 20 points."
Playmaker Dimitris Diamantidis led the winners with 23 points, including an audacious three-pointer on the buzzer which silenced the vociferous home crowd.