Russia fell behind 74-72 on Marcelo Huertas' layup with 6.1 seconds left. Russia called time-out and threw the ball to Fridzon along the left corner, who knocked down the jumper to hand Brazil its first loss in three games.
"The coach told me if I was open, shoot it. So I shot it," Fridzon said.
Earlier, San Antonio teammates Tony Parker and Manu Ginobili put on separate clinics to lead their teams to important wins.
Parker scored 27 points and Nicolas Batum added 21 to lead France to an 82-74 victory over Lithuania.
Ginobili scored 24 points and keyed a second-quarter run to help Argentina beat Tunisia 92-69.
France and Argentina are now both 2-1 in Group A, while Russia tops Group B. The top four teams from each of the six-team pools advance to the quarterfinals.
Andrei Kirilenko scored 19 points and Timofey Mozgov had 18 for Russia in its third straight victory, but it was Alexei Shved who led the Russians' late rally after they fell behind by five with under two minutes left. Shved, headed to the Minnesota Timberwolves along with Kirilenko, finished with 17 points.
Leandro Barbosa scored 16 points and Larry Taylor had 12 for Brazil (2-1). Nene finished with eight points and 10 rebounds.
Kirilenko, who came in leading the Olympics in scoring with 25.5 points per game on a tournament-best 72.4 per cent shooting, had only five points after halftime, part of the reason Russia nearly blew a second-half lead.
Kirilenko, the longtime Utah Jazz forward, stayed in Russia with CSKA Moscow last season and was MVP of the Euroleague.
Trailing by 11 late in the third quarter, Brazil battled back to tie it at 63 midway through the fourth on Barbosa's basket. Mozgov's follow shot put Russia back on top, but three straight free throws, the last two by Nene, gave the Brazilians a 66-65 edge with 3:40 to play. Taylor and Barbosa followed with baskets in the lane, extending the lead to 70-65 with 2:25 remaining.
It was still a five-point game before Shved hit a a jumper, and after he missed two free throws, Russia got the ball back after a turnover and he nailed a 3-pointer that tied it at 72 with 26 seconds left.
Huertas drove left and scooped in a right-handed layup, but that left just enough time for Russia to win the closest game so far.
Parker, wearing goggles to protect an eye injured in a nightclub brawl, sank a 3-pointer to finish a 10-2 run that gave France a 59-52 lead at the end of third quarter and Lithuania never got closer than six after that.
"My legs felt very good today. I was able to run, penetrate, score," said Parker, who scored seven of France's last eight points.
Ronny Turiaf of the Los Angeles Clippers pulled down 10 rebounds for France (2-1), which was led by the NBA players on its roster. Batum plays with the Portland Trail Blazers.
Reserve Martynas Pocius led Lithuania with 18 points. Linas Kleiza, who plays for the Toronto Raptors, added 17.
"We played well for about 30 something minutes but we came up short unfortunately," Kleiza said.
France coach Vincent Collet said Parker and Batum are picking up their games.
"This is the first game we've had them at this level. Tony told me that his legs were feeling a lot better now," Collet said.
Parker was an innocent bystander at the bottle-tossing melee in New York in June. His left cornea was scratched and he feared he might miss the Olympics.
Lithuania (1-2) needs a win, but next up is the U.S.
"We are going to play as hard as we can," coach Kestutis Kemzura said. Lithuania is a three-time Olympic bronze medallist .
"We played a good game today but not enough minutes. They got some easy baskets and Tony took over in the second half," Kemzura said.
Earlier, Tunisia led by 14 after the first quarter against Argentina. But Ginobili scored 12 points in a 15-0 run at the start of the second quarter that gave Argentina a 29-28 lead.
Tunisia battled back and the game was tied 40-40 at halftime but Ginobili hit a 3-pointer to start the second half and Argentina never trailed again.
Carlos Delfino added 21 points and Luis Scola had 20 as Argentina's NBA stars pounded winless Tunisia. Scola plays for the Phoenix Suns and Delfino is with the Milwaukee Bucks.
Salah Mejri finished with 19 points for Tunisia and Mourad El Mabrouk had 16.
Also, Patty Mills scored 20 points to lead Australia to an 81-61 victory over winless China for its first win.
Wang Shipeng finished with 21 points for China, all of them from 3-pointers. He made seven of 10.
AP Basketball Writer Brian Mahoney contributed to this report.