Anadolu Efes led 47-37 before the break and retained a six-point lead, 68-62, at the end of the third quarter at Istanbul's Sinan Erdem Sports Hall.
With 7:30 left in the fourth, Turkish center Sertac Sanli, 30, scored a three-pointer to give Barcelona a 69-68 lead.
He made it 72-68 after hitting another three-point shot.
Barca were leading 80-78 with 20 seconds remaining when Anadolu Efes playmaker Shane Larkin was fouled.
Larkin sunk a pair of free throws to tie the game at 80 as time ran out.
Once overtime began, Sanli scored to give Baca a 2-point lead. And they never looked back.
It was a close matchup in the last two seconds as Anadolu Efes' French forward Adrien Moerman scored a three-pointer to narrow the gap to a single point, 94-93.
Then Anadolu Efes made a tactical foul against Sanli to stop the clock, sending him to the free-throw line.
The Turkish player made the first free throw but intentionally missed the second to drain the clock.
Anadolu Efes' Krunoslav Simon grabbed the rebound and did not waste time in taking a full-court shot that missed before the clock expired.
Barcelona extended their winning streak to five games in the 2021-22 EuroLeague regular season.
The team has 11 wins and just two losses to top the EuroLeague standings.
Anadolu Efes are now 10th in the standings with a 6-7 win/loss record.
The Turkish team's four-game winning streak ended with the loss.
Sanli, who is a former Anadolu Efes player, scored 24 points in the Spanish victory.
Anadolu Efes was led by Serbian guard Vasilije Micic, 27, who racked up 26 points.
Friday's results:
UNICS Kazan - Olympiacos: 84-87
Anadolu Efes - Barcelona: 93-95
Zenit - Crvena Zvezda mts Belgrade: 58-69
ALBA Berlin - AX Armani Exchange Milan: 81-76
