Six-times winners CSKA ground out a dramatic 73-71 victory at Gescrap Bilbao to beat the Spanish side 3-1 and 1997 champions Olympiacos overcame Montepaschi Siena 76-69 at home to complete a 3-1 win over the Italian team.
They joined 2010 winners Barcelona, who qualified with a 3-0 sweep of Russians Unics Kazan. Holders Panathinaikos Athens host Maccabi Tel Aviv in a decisive fifth game on Tuesday with their series tied at 2-2.
Former Utah Jazz forward Andrei Kirilenko produced a performance worthy of his NBA prime, pouring in 23 points and collecting eight rebounds as CSKA held off a spirited challenge by Euroleague debutants Bilbao.
Kirilenko hit a treble of three-pointers and buried most of his shots at critical moments when Bilbao, roared on by a fervent 9,000 home crowd, threatened to swing the enthralling contest their way.
In Athens, Olympiacos fans lit flares in the team's Peace and Friendship Arena after Kyle Hines and Vassilis Spanoulis scored 19 points each to down Siena, who missed their injured forward Bootsy Thornton.
Siena maintained a slender lead through the opening three quarters but lost out in a furious finish as playmaker Spanoulis sealed the series with an audacious three-pointer.
The contest between Panathinaikos, aiming for their seventh title, and last season's runners-up Maccabi produced the expected titanic tussle between two of Europe's most heralded heavyweights in the last two decades.
Having taken a 2-1 lead in the series with a 65-62 win on Tuesday, five-times Euroleague winners spurned a gilt-edged chance to wrap up the series after throwing away the lead in the closing stages of Game 4 on Thursday.
Trailing 67-66 with three minutes left in Maccabi's Nokia Arena and facing a deafening roar from the frenetic home fans, Pantahinaikos showed all their resilience in a late run to win 78-69 and take the slugfest back to Athens.
"Everything that has happened in this series has given a lot of people in Europe great entertainment and they will be happy to see another game," Panathinaikos coach Zeljko Obradovic told the competition's website.
"Some people had already written us off and they forgot that we are the European champions, but I enjoy coming to this Arena every time and hope to be back soon," said the 52-year old Serb who won eight Euroleague titles with four different clubs.
Five of them came with Panathinaikos whose depth on the bench could make the difference in the home straight, although Maccabi coach David Blatt tried to remain upbeat about his team's chances.
"I told my players I am proud of them more than any coach can be proud of his players, we will keep our heads up and go to Athens with a desire to win although it will be one of the toughest games in the club's history," he said.
The Final Four will be held in Istanbul from May 11-13.