Second-half goals from Portuguese midfielder Zeca and Jean-Alain Boumsong gave the struggling Athens giants a two-goal lead before Anastasios Karamanos netted a last-minute consolation at the Peristeri Municipal Stadium.
It was the first league win for Panathinaikos since Dec. 2 and the first since Fabri this month became their third coach of the season, following Jesualdo Ferreira and Juan Roman Rocha.
"The team deserves a place in the end of season playoffs," Spanish striker Toche told reporters. "No team has shown they are better than us and I believe we have simply been really unlucky this season.
"I think we can succeed and get a place in Europe because we are working so hard. It's something I believe we and our fans deserve."
The win moved the Greens up to seventh place although another victory for runaway leaders Olympiakos Piraeus meant the gap between the two teams remained a massive 26 points.
Chilean defender Pablo Contreras hit the only goal of the game for Antonis Nikopolidis's champions as Olympiakos brushed off the recent departure of captain Vasilis Torosidis to AS Roma with a 1-0 win over Panthrakikos in sub-zero temperatures in Komotini.
"I am pleased with the desire of my players. I could not have asked for more from them...it may be early but I am seeing my team implement a lot of things I have been trying to get across to them," said Nikopolidis who has won two games in a row since taking over from Leonardo Jardim.
Olympiakos are yet to lose this season and have collected 51 points from 19 matches.
The Reds hold a commanding 14-point lead over Asteras Tripolis who leapfrogged PAOK Salonika into second spot following a resounding 3-0 win at Platanias.
PAOK boss Giorgos Donis lamented his team's lack of intensity as they slumped to a 1-0 home defeat against lowly Xanthi.
"We have to get it into our heads that from here on in the team will be strengthened and we can kick on," he said.
"The new players Katsouranis and Schildenfeld we have brought in but have not yet played will now raise the level to where we want to be and we will work to change our style of play."
Striker Antonis Petropoulos scored his third goal since joining AEK Athens from Panathinaikos as Ewald Lienen's team climbed further away from trouble with a 2-1 home win over OFI Crete on Saturday, their fifth victory of the season.