The Greek side, led by Mike Batiste on the night, will take home court advantage into the play-offs thanks to their 4-2 Top 16 record.
Batiste poured in 12 points while Sarunas Jasikevicius added 10. Henry Domercant led Unics, who also go through, with 19.
Pana now meet Israeli champions
Victory for Barca - their seventh consecutive win - means the Spanish outfit are the only side to finish the Top 16 with a perfect record.
Pete Mickeal paced the winners with a season-high 20 points as Barca geared up for their next challenge against Unics in style.
Malik Hairston led the Italian team with 27 points - a career best - as they finished their Group G campaign with a 3-3 record and three consecutive wins under their belt.
Fenerbahce needed victory to advance to the play-offs, but defeat sent Unics through at their expense.
In Group H,
Both sides had already been eliminated from play-off contention, but that did not detract from an entertaining game in Lithuania.