Trailing strong favourites CSKA Moscow 53-34 midway through the third quarter in the final, Olympiacos dug deep and completed a stunning fightback after Gergios Printezis scored on the buzzer to give them a 62-61 win.
Having had their budget cut by the economic crisis in Greece, Olympiacos first defied the odds to reach the playoffs and the arrived to the Final Four as the least heralded team to win the showpiece event in Istanbul.
Led by their Serbian coach Dusan Ivkovic, a trophy-laden tactical maestro in his second spell in charge of Olympiacos, the Greek outfit upset 2010 winners Barcelona in the semis before overpowering six-times winners CSKA.
"I have to thank my players, the staff and our incredible fans who stuck with us through the thick and thin, this victory is a result of tremendous will-power and a monumental effort to achieve the impossible," Ivkovic told a news conference.
Cutting an incredibly calm figure after the most dramatic of wins, the 68-year old coach added: "CSKA were the obvious favourites not just today but throughout the season and it was our iron-clad defence that turned the match.
"Of course it helped that I coach CSKA's fellow Serbs Milos Teodosic and Nenad Krstic in the national team, the former got off to a great start and was their best player but we staged a hardly explicable fourth quarter fightback."
After a cagey opening dominated by defensive play, CSKA romped to a 25-13 lead on the back of a treble of successive three-pointers by Teodosic and looked in complete control until the final period.
A twist in fortune looked all the more unlikely because CSKA beat Olympiacos emphatically in both regular season meetings, having won one of them by a whopping 32-point margin in Moscow.
But their offence came to a screeching halt at crunch time while Vassilis Spanoulis, named the tournament's most valuable player, started hitting jump-shots and dishing out assists to his team mates at the other end.
CSKA were still in the driving seat after former Utah Jazz forward Andrei Kirilenko gave them a 59-52 lead in the closing stages but missed free throws and turnovers cost them dearly.
Forward Ramunas Siskauskas missed two foul shots with 10 seconds left and Spanoulis found the unmarked Printezis on the baseline to beat the buzzer and throw 5,000 ecstatic Olympiacos fans into raptures.
"Spanoulis was our driving force throughout the Final Four but it was our team spirit and die-hard attitude that turned the match on its head," the Greek outfit's Macedonia centre Pero Antic told Reuters.
"We never stopped believing in ourselves even when we were 19 points down, we knew we could get back into the game if we carried on playing strong defence and we got our reward."
For Ivkovic, it was a gratifying finale as he won the second Euroleague title with Olympiakos after guiding them to their first success in Europe's elite competition in 1997.
"Now we will party, have a few days' rest and prepare for the Greek league's final series against Panathinaikos, it will be like another Final Four," said Antic.
"With a bit of luck, we will repeat the trick and give Ivkovic the same kind of joy he tasted 15 years ago."