A fantastic first half free-kick from Laurent Robert put Newcastle 2-1 ahead at half-time after Predrag Djordjevic’s penalty had earlier cancelled out Alan Shearer’s spot kick opener.
Patrick Kluivert ensured The Magpies travelled back to Tyneside with a two goal advantage when he shot home after good work by Milner after 69 minutes.
Olympiacos were reduced to nine men in the first half after Grigoris Georgatos was dismissed for his foul on Dyer in the lead up to the penalty and then Kostoulas was given his marching orders for a second booking.
The win leaves Graeme Souness’ men in a strong position going into the second leg next Wednesday.
Newcastle