Inspired by a vocal travelling support who defied Greece's economic problems to make the trip to London, Olympiakos battled back from 27-10 down after the first quarter of the Euroleague final to take the lead early in the second half.
They rarely looked threatened, shooting 39 points in the fourth quarter to clinch their third Euroleague title 100-88.
"(Madrid) scored some incredible shots in the first quarter, but we put a stop to that and started rebounding offensively, and I think that was the key to success in the end," said Olympiakos forward Pero Antic.
The win was in a stark contrast to last year when it took a game-winning shot from Georgios Printezis at the buzzer to overcome CSKA Moscow.
Having defeated much-fancied CSKA again in Friday's semi-final, the Greeks started slowly on Sunday and struggled against Madrid's sharp shooting in the first quarter.
But Olympiakos' trademark ironclad defence soon kicked in, allowing eight-times champions Madrid just 14 points in the second quarter and 20 in the third as Kyle Hines and Pero muscled out the Spanish forwards inside the paint.
The team's talisman Vassilis Spanoulis dominated the second half, shooting a total of five three-pointers and notching up four assists. He was voted the Final Four's most valuable player for the third time and finished top scorer with 22 points.
"It has been a very difficult year - you know our budget," Spanoulis said. "Our backs have been against the wall many times, but we have stayed together and fought back each time."
A 21-point haul for Rudy Fernandez, who quit the National Basketball Association to return to Madrid last year, could do little to stem the tide.
"Spanoulis' three pointers changed the game's rhythm while we were still working to get back into the game, but in the end they were able to control the (lead)," said Real coach Pablo Laso.
Earlier, Barcelona's Marcelinho Huertas missed a potentially game-winning shot at the buzzer, letting CSKA hold on for a 74-73 victory in the league's third place play-off.