Saviola scored twice and missed a spot kick as the Greek side beat eight-man Anderlecht 3-1, with Vladimir Weiss also failing with a penalty before Alejandro Dominguez made it third time lucky from 12 yards in the last minute.
Olympiacos could have done without the stress on a night when they needed to win to assure themselves of progression but, even though Sacha Kljestan scored for Anderlecht, Saviola's old club Benfica were made to settle for the Europa League as Olympiacos progressed.
It was a crazy night added to even more by the trio of red cards shown to Anderlecht's players. Cheikhou Kouyate was the first to go just after half-time, with Fabrice N'Sakala and excellent goalkeeper Silvio Proto following late on.
Proto's dismissal was particularly harsh given his brilliance in the match, saving two penalties and making plenty more stops. The irony was his sending off caused the penalty which was scored.
With nothing to play for Anderlecht's start was admirable, as Aleksandar Mitrovic drilled wide and Dennis Praet had a shot blocked.
Olympiacos woke up and Paulo Machado drew a fine stop from Proto with a stunning 30-yard free-kick that deserved a goal.
Joel Campbell was also denied by Proto and Saviola skewed wide, before finding his range with 33 minutes gone as he converted in the wake of David Fuster's shot being blocked.
That could have been the signal for Anderlecht to wave the white flag but six minutes later they were level as Guillaume Gillet's pass was tucked away by Kljestan.
Campbell sensed the opportunity for a second before the break and was unlucky to see a shot go wide, but there was no bad fortune involved as Michael Olaitan nodded over when it appeared easier to score.
The first half had been lively but the start to the second topped it.
Kouyate handled in the box as he tried to deal with a Fuster shot - he walked as a consequence - and Saviola stepped forward and drove it high, but at a reachable height for Proto who punched it away.
Saviola could have been forgiven for thinking his miss would be costly but he was making amends in the 58th minute, powering in a Fuster cross from close range.
A standing ovation followed for Saviola as he was taken off, with the same treatment afforded to Roberto as he made a fine stop to deny Gillet.
Weiss then had the chance to make it three when he stepped up after being tripped, but Proto was equal to his penalty, saving with his legs.
Olaitan was then denied by the stopper, before N'Sakala saw red for a second booking as he tripped Weiss.
The former Rangers man was causing all sorts of problems and it was he who was dragged down by Proto in time added on, causing a third red, a third penalty and finally a success as Dominquez got the job done, with Mitrovic taking on the gloves to no avail.