Finland, playing in their first major event since the Eurobasket in 1995, also upset Bosnia 92-64 while Slovenia struggled for three quarters against Georgia before pulling away in the final period to register an 87-75 success.
Croatia beat Montenegro 87-81 and Russia's reserve shooting guard Vitaliy Fridzon enjoyed a memorable evening as he led his team to a 79-58 thrashing of Belgium with 22 points.
Macedonia, having lost to double European champions Greece by 32 points at the 2009 European Championship, pulled off the biggest surprise of the tournament so far after showing how much they had improved in Thursday's 78-76 win over Croatia.
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Led by American-born point guard Bo McCalebb, who scored a game-high 27 points, the Macedonians blew away their bigger neighbours as centre Pero Antic added 12 points and eight rebounds for the winners.
"We played in a state of trance and our defending was quite simply fantastic. This win means a lot to us because we have given the whole nation a huge lift," Macedonia coach Marin Dokuzovski said.
"I am sure the whole of Macedonia will celebrate tonight but we can't get carried away because we have a difficult game against Finland who have also proved their worth," he added.
About 5,000 people, sporting national flags and setting off fireworks, gathered in Skopje's central square to celebrate and more were expected to arrive during the night.
Macedonia has strained political ties with Greece because of a dispute over the former Yugoslav republic's name, which is the same as a province in northern Greece where Alexander the Great was born.
Many fans who descended on the square said beating Greece meant more to them than the unlikely prospect of winning the 24-team tournament in Lithuania, which Macedonia entered as rank outsiders.
"I am a Macedonian expatriate living in Australia on holiday here and when I go back I will give my Greek friends more banter than they can possibly take," 40-year old Tome Tomevski told Reuters.
"We argue over politics all the time but there will be no dispute over this because our boys played them off the court.
"As far as I am concerned, they don't have to win another match," he said. "They can return home tonight to join the party which appears set to last until the morning."
There was also plenty of joy for the Finns, who rekindled their own hopes of reaching the second group stage after five players finished with double scoring figures against Bosnia.
Point guard Mikko Koivisto scored 17, playmaker Petteri Koponen had 14, centre Gerald Lee added 12 while forwards Hanno Mottola and Tuukka Kotti hauled 10 each to cancel out a good solo effort by Bosnia's Henry Domercant, who put on 25 points.
Croatia stayed on course to reach the second group stage, featuring two groups of six, after centre Ante Tomic scored 26 points to fend off a spirited challenge by neighbours and fellow former Yugoslavs Montenegro.
Point guard Marko Popovic added 23 points for the Croatians, who joined Greece and Macedonia at the top of Group C with a 2-1 record, ahead of Finland, Montenegro and Bosnia who have one win and two defeats each.
Slovenia and Russia have three wins out of three in Group D while Ukraine registered their first with a 67-59 victory over Bulgaria.
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Russia and France into semis