Vincent Aboubakar's dismissal did not prevent 10-man Besiktas from moving into the quarter-finals of the UEFA Europa League as Ryan Babel struck twice in a 4-1 home win against Olympiacos.
Besiktas had a narrow advantage from the first leg after netting an away goal in the 1-1 draw in Greece and they soon took a further step towards the last eight through Aboubakar.
The forward's downward header from a floated Anderson Talisca centre got the Turkish side off to a flying start and their lead was soon doubled from another right-wing cross.
Ricardo Quaresma provided the assist this time, Babel controlling before lashing in a shot through a crowd of bodies that goalkeeper Nicola Leali perhaps should have saved.
Besiktas seemed to be cruising but the visitors gave themselves hope when Tarik Elyounoussi's acrobatic volley deflected in at the near post after 31 minutes and momentum appeared to swing when Aboubakar was sent off before the interval for violent conduct after clashing with Takis Retsos.
But Olympiacos could not make their extra man count and when Babel grabbed his second of the game and Cenk Tosun scored from the bench, their bid to reach the last eight of the competition for the first time failed, with Besiktas now unbeaten in their previous eight European home games.
Quaresma forced the first save of the game, the winger's free-kick beaten away from the top-left corner by Leali.
And the hosts' bright start led to the opening goal inside 10 minutes, Aboubakar again on target with his fifth European goal of the season.
The Cameroon striker scored the equaliser in the first leg and he pounced after a period of Besiktas pressure, heading home Talisca's right-wing cross to put his side in front.
Besiktas soon looked to be in total control as Babel doubled their lead after 22 minutes when Quaresma's cross found the Netherlands international in the box and his shot had too much power for Leali.
Olympiacos had barely threatened when a spectacular goal from Elyounoussi got the Greek champions back in the tie with their first shot.
Aly Cissokho stood up a cross to the back post and Elyounoussi's scissor-kick volley took a small deflection off Adriano to beat Fabri in the Besiktas goal.
Besiktas's narrow lead became even more precarious when Aboubakar was dismissed for senselessly aiming a headbutt at Retsos six minutes before half-time.
Fabri turned Konstantinos Fortounis's free-kick over the crossbar after 58 minutes as the visitors sought to make their numerical advantage pay, then Quaresma bent a shot wide on the break.
With Olympiacos committing men forward Besiktas wrapped up the tie with another incisive counter-attack with 15 minutes to play, Babel's low shot squirming under Leali's weak right hand.
And gloss was added to the scoreline by Tosun two minutes after his introduction, the striker dinking neatly over Leali after timing his run onto Talisca's pass to bring up his 20th goal of the season and send Senol Gunes's men through to the quarter-finals for the first time since 2002-2003.