Two goals from Greece defender Avraam Papadopoulos and one from Algerian winger Djamel Abdoun enabled Olympiacos to overpower AEK and seal the Super League title as the Reds hold a 16-point lead over Asteras Tripolis with five matches left.
The result came on the anniversary of the club's founding 88 years ago.
Olympiacos are also through to the quarter-finals of the Greek Cup and remain on track for the domestic double.
There was an expectant atmosphere in Piraeus ahead of kick-off with the club showing a video of the team's past glories on two large screens inside the stadium.
Papadopoulos, who has missed most of the season with an ankle injury he suffered at Euro 2012, prodded home from close range in the 14th minute from Rafik Djebbour's knock-down, and then doubled the lead in the 56th minute when he headed home Jose Holebas's left-wing cross.
AEK passed up two decent chances to get back into the game and the match was put beyond doubt two minutes after the hour mark when Djebbour surged down the right and crossed for compatriot Abdoun to slot home from close range.
"I am delighted that I have come back into the team after such a long time out and that my return has coincided with winning another league title," a jubilant Papadopoulos told reporters.
"I've only scored a few goals in my career so it is always nice but they pale in comparison to winning a title and the 40th one in the club's history at that. For me the team comes before anything else... I have gone through a very tough time with my injury but football is like that sometimes and it can often make you stronger."
Olympiacos striker Djebbour, who has 20 goals this season and is set finish as the Super League's top scorer, created two goals on the night.
"It's been a fantastic week as I also had my birthday and the title was the best gift I could receive," said Djebbour, who turned 29 on March 8.
"We are worthy of the title as I think we have shown that we are the best team and I am very happy that we are champions... Today I was not able to score, but I provided two assists so I am happy for what I can offer in other areas of the pitch."
While Olympiacos celebrated, the defeat leaves Ewald Lienen's struggling AEK just one point and one place above the relegation zone having collected 26 points from 25 matches.
Bottom club Kerkyra, who were beaten 1-0 by Panathinaikos on Saturday, continue to look isolated with just 20 points, while Aris, who occupy the second relegation spot in 15th, gave their survival hopes a shot in the arm with a 4-0 home win over Levadiakos on Sunday - a result which moved them on to 25 points.
The focus now shifts to the race for places in the Super League playoffs, which involve the teams who finish from second to fifth.
Asteras Tripolis continued their excellent form with a 1-0 home win over Panthrakikos to cement their grip on second spot, but they are only one point ahead of PAOK Salonica, who were 2-1 winners at Platanias on Saturday.
Despite an indifferent campaign due to financial problems, Panathinaikos maintained their fragile hold on fifth place with a narrow 1-0 home win over Kerkyra thanks to Luciano Figueroa's 78th-minute penalty.
However, the Greens will face a fight to the finish in the final playoff spot as PAS Giannena are level on 35 points with Fabri's team following their 1-0 win at Skoda Xanthi on Sunday.