Jose Mourinho's first European game and first home match at the Spurs helm began miserably but Dele Alli, Aurier and a Harry Kane brace saw them produce a blistering response and confirm a spot in the last 16 for last season's beaten finalists.
A brilliant start by Olympiacos left Spurs stunned as Youssef El-Arabi and Ruben Semedo had the visitors two up by the 19th minute, only for a defensive lapse to hand Spurs a way back through Alli's first Champions League goal in two years.