New signing Danny Shittu made his Trotters debut but lost central defensive partner Cahill within 20 minutes when the former Aston Villa player was adjudged to have brought down Juanfran.
The red card completed a frantic opening for Wanderers, who were also thankful for Jussi Jaaskelainen's 10th-minute penalty save from Rivaldo - after Jlloyd Samuel had fouled Ignacio Scocco.
In the 17th minute, the English side fell behind to what would prove the decisive blow when Perparim Hetemaj blasted home a brilliant 25-yard shot via the crossbar.
Samuel volleyed just wide, but the Greeks were utterly dominant in the first half amid a lively atmosphere at the Olympic Stadium.
Ricardo Vaz Te and Andy O'Brien came close in the dying moments, but Bolton were deservedly beaten.