Panathinaikos, who are on to their third coach this season in Spaniard Fabri, fell behind to Serge Die's superb long-range goal five minutes before half-time and could not find a response in a lethargic display.
They are now without a win on home soil since the 2-0 victory over PAOK Salonika on Nov 18 and Fabri's team dropped to joint-eighth in the table with 26 points from 21 matches, while Xanthi leapfrogged the Greens and are now in sixth spot.
"I feel sad and depressed frankly," Fabri said.
"I can not understand how a team with such a proud history has ended up like this. After two good performances in recent games we were awful in every department, with or without the ball.
"I can't explain how we are playing better away from home, perhaps its down to the fact that we don't have to chase games and work has hard in terms of trying to open teams up."
Panathinaikos are now 28 points behind arch rivals and league leaders Olympiakos Piraeus, who returned to winning ways on Saturday with a vital 1-0 away win at third-placed Asteras Tripolis thanks to Kostas Mitroglou's solitary goal.
The match marked a successful debut for new coach Michel after the Spaniard signed a two-year contract on Feb. 4 to replace Portuguese coach Leonardo Jardim.
Olympiakos, the reigning champions, extended their lead over PAOK by 15 points and look odds on to claim a 40th league title.
AEK Athens midfielder Roger Guerreiro believes the cash-strapped club can start looking up the table again after his first-half penalty proved enough to claim a 1-0 win for the Yellows at Kerkyra on Sunday.
Ewald Lienen's team, who struggled for the early part of the season, are currently enjoying a rich vein of form after recording what was a third successive victory and are now seven points clear of the relegation zone in 12th place.
"It was a very important win for us and at the moment we are in a good place psychologically heading into the latter part of the season," said Guerreiro.
"I'm 100 per cent sure that AEK will stay up," added the naturalised Poland midfielder.
"We did not have a good first half of the season and we did not have luck on our side but now we are getting a bit of good fortune as well as playing some good football so now I'm only looking up the table."