Anadolu Efes' US-born Turkish playmaker guard Shane Larkin scored 28 points, had eight assists and four steals for the Turkish team.
ALBA Berlin's German forward Oscar Da Silva was his team's top scorer with 20 points.
In the Round 33 game at Istanbul's Sinan Erdem Sports Hall, ALBA Berlin led after the first quarter 24-16 but Anadolu Efes fought to narrow the lead to single digits before the break to 36-39.
Anadolu Efes took a 54-52 lead when French forward Adrien Moerman hit a three-pointer with three minutes and 39 seconds remaining in the third quarter.
By the end of the stanza, the Istanbul team were 62-57 in front thanks to Elijah Bryant and Larkin's prolific performances.
In the fourth period, the score was tight; it was 75-73 for Anadolu Efes with three minutes and 19 seconds remaining to the final buzzer.
Then Larkin scored a three-pointer to make it 78-73, giving momentum to Anadolu Efes.
The Turkish team controlled the game in the final three minutes and a playoff ticket.
Fifth-place Anadolu Efes had their 15th win in the 2021-22 EuroLeague regular season. They have previously lost 11 games.
The Istanbul club will play two more games to conclude the regular season -- Bayern Munich in Istanbul on April 6 and Crvena Zvezda in Belgrade on April 8.
ALBA Berlin are currently in the 10th spot at 11-15.
The German club have been eliminated.
In the next fixtures, ALBA Berlin first will take on Panathinaikos OPAP on April 6, then will visit France's Monaco on April 8 to end the season.
Only the top eight teams qualified for the EuroLeague playoffs that will start April 19.
Barcelona (Spain), Olympiacos (Greece), Real Madrid (Spain), AX Armani Exchange Milan (Italy), Anadolu Efes (Turkiye), Maccabi Playtika Tel Aviv (Israel), Monaco (France), and Bayern Munich (Germany) reserved their places for the playoffs.
Meanwhile, Bitci Baskonia Vitoria-Gasteiz (Spain), ALBA Berlin (Germany), Crvena Zvezda mts Belgrade (Serbia), Fenerbahce Beko (Turkiye), Panathinaikos OPAP (Greece), LDLC ASVEL Villeurbanne (France), and Zalgiris Kaunas (Lithuania) have been eliminated.
