Leonardo Jardim's team went into the match on the back of seven straight victories but the visitors were behind twice and had to rely on an 83rd-minute equaliser by Greece defender Jose Holebas with the hosts down to ten men.
Manolis Papasterianos gave Aris the lead after three minutes only for Djamel Abdoun to level from the penalty spot six minutes later before David Aganzo's 79th minute strike restored the hosts lead over the champions.
However when Nikos Psychogios was dismissed for a second bookable offence with nine minutes remaining it was 12th-placed Aris hanging on as Olympiakos, who top the table with 22 points from eight games, fought back through Holebas' equaliser.
Panionios are second on 18 points and PAOK Salonika third with 17 while Panathinaikos continue to struggle in ninth with nine points following their 2-2 draw against OFI Crete on Monday where they were twice in front.
There was joy for bottom club AEK Athens on Sunday as the club picked up a vital first win of the season against Platanias, new coach Ewald Lienen's second game in charge.
AEK moved to within a point of 13th-placed Panthrakikos, Xanthi (14th) and second-bottom Levadiakos and have a better goal difference than all three clubs.