Manolas put the home side ahead after 13 minutes but Roberto made a string of saves to keep the lead intact.
Benfica had the first attempt but Oscar Cardozo could not find the opening after four minutes as Dimitrios Siovas made the block.
Cardozo tried his luck again two minutes later but Roberto made a good save for the home side.
Lazar Markovic continued the away side's good start with another shot on goal but Roberto was again equal to it.
Konstantinos Mitroglou had Olympiakos' first attempt on goal after 10 minutes but Artur made a save.
And when Jose Holebas took a 13th-minute corner Manolas powered in a downward header to give the home side the lead. Artur got a hand to the ball but could not keep it out of the net.
Benfica had a chance to hit back when Andreas Samaris fouled Enzo Perez but the Benfica player did not make the most of the free-kick as he missed the target after 22 minutes.
Just before the half hour a Perez corner found Benfica captain Luisao but his header from close in skimmed the top of the bar.
A long-range volley by Sambou Yatabare was just over the bar as Olympiakos looked to stretch their lead.
Three minutes before half-time a Perez corner reached Nemanja Matic but he missed the target from close range.
Lazar Markovic had a shot on goal a minute into the second half but Roberto made a save with his feet.
As Benfica pressed for an equaliser Maxi Pereira was off target with a looping header before Roberto denied Silvio with another save.
And just before the hour Perez was on target with a volley but Roberto got down well to save.
With just over 20 minutes to go Roberto made a save when substitute Filip Djuricic saw his powerful shot kept out.
And with two minutes to go the Olympiakos keeper again came to his side's rescue as he dived at the feet of Djuricic to gather the ball.