Belgian striker Kevin Mirallas opened the scoring for the Reds two minutes before half-time with a neat finish from Albert Riera's pass.
The home side equalised through Vaclav Sverkos, the ball ricocheting off the Czech striker from Francois Modesto's attempted clearance and looping in.
Olympiakos' performance was soured in the 73rd minute when former Liverpool winger Riera was dismissed for kicking out at Giannis Kontoes, but the result preserved their 10-point lead over second-placed Panathinaikos with six matches to go.
Struggling Panionios moved one point clear of the relegation zone.
Riera, the Spanish winger, apologised for his red card after the game. "I apologise to all my team-mates for my sending-off, I don't usually lose control like that," he told reporters.
Jesualdo Ferreira's Panathinaikos, still affected by last weekend's derby defeat to their Athens rivals, drew 1-1 at home to Atromitos on Saturday.
Brazilian midfielder Brito put the visitors in front after 31 minutes, but the lead lasted just two minutes before French striker Sidney Govou, given a rare start, equalised.
Also on Sunday, AEK Athens leapfrogged Olympiakos Volos into third place with a 3-2 away win over Ergotelis in Crete, while PAOK Salonika slumped to a 2-0 home defeat to Kavala.
