Fuchs struck with 13 minutes remaining as the Bundesliga side finally broke down a stubborn Olympiakos side who had little ambition other than to stifle their hosts. It means Schalke are top of Group B, one point ahead of Arsenal, with one game remaining.
It was Schalke who made the better start on the attacking front, Klaas Jan Huntelaar firing over from close range.
They were inches away from going ahead in the 10th minute when Lewis Holtby fired in a shot from 25 yards which rattled the bar but went to safety.
Djamel Abdoun fired over as Olympiakos showed as an attacking force but again it was the hosts who came closest to making the breakthrough.
Leandro Greco fouled Huntelaar on the right and from the resulting free-kick, 25 yards out, Fuchs forced visiting goalkeeper Roy Carroll to tip the ball round the post.
Julian Draxler, Roman Neustadter and Jefferson Farfan all had shots blocked as Schalke dominated while Huntelaar volleyed wide.
The Greek side had shown next to nothing as an attacking entity but somehow they made it to half-time without their defence having breached and in reality were quite comfortable.
The second half started much the same as the first, Olympiakos containing Schalke with Carroll comfortably gathering headers from Kyriakos Papadopoulos and Huntelaar.
Home goalkeeper Lars Unnerstall had been a virtual bystander for the game but finally, with a little under 20 minutes to go, he was called upon, tipping Ricardo Paulo Machado's shot from the right around the post.
However, that did not herald more attacking from the Greek side but instead the hosts finally made the breakthrough 13 minutes from time, Fuchs firing home from 30 yards into the bottom right-hand corner of the goal.
Draxler's shot was blocked by Carroll with the keeper then thwarting Huntelaar with his feet. Machado's curling shot failed to test Unnerstall as Olympiakos made a rare foray forward and Carroll was again called upon, this time repelling Teemu Pukki's shot with his feet.