The Euroleague's all-time leading scorer Juan Carlos Navarro netted 15 points and Brazilian point guard Marcelinho Huertas added 10 to give Barca a 3-2 win in a rollercoaster best-of-five quarter-final play-off series, while forward Stephane Lasme stood out for the visitors with 16 points.
"The fans made it a magical occasion, packing the Palau Blaugrana to make a great atmosphere," Barcelona coach Xavier Pasqual told the competition's official website.
"For me, to celebrate 100 games in charge of Barcelona with qualification for the Final Four is ideal and now we will recuperate to gather our strength for what awaits in two weeks."
The result has set up a mouth-watering clash between Barcelona and their traditional Spanish rivals Real Madrid, while six-time winners CSKA Moscow will meet either holders Olympiakos Piraeus or Anadolu Efes Istanbul.
Olympiakos and Anadolu meet in a decisive game five on Friday.
Barcelona led 28-14 after the opening period and although Panathinaikos pulled back to within six points in the final quarter, the Catalan side held off after Navarro nailed a long-range effort to throw the home fans into raptures.
"We knew it would be a complicated game but we won and that's all that matters," said Navarro, who steered Barcelona to the 2010 success when they beat Olympiakos in the final.
"We must rest now because we took it to the limit, physically speaking."
Barcelona will get a dress rehearsal of their bid to win their third Euroleague title when they visit Real in a Spanish league derby on Sunday.
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- Juan Carlos Navarro