Hoewedes headed in a corner from Jefferson Farfan in the 41st minute. That came only moments after Schalke's Greek defender, Kyriakos Papadopoulos, had a similar goal disallowed for a foul on goalkeeper Balazs Megyer.
"I'm very happy with the goal and the result. We took our chances," Hoewedes said. "It was great to get this against such a team and such a home crowd."
Papadopoulos played a vital role in holding off Olympiakos early in the first half, clearing a goal-bound shot from Paulo Machado in the fifth minute.
In the second half, Djamel Abdoun levelled for Olympiakos in the 58th after finishing off a move started by fellow Algerian Rafik Djebbour, who slipped in front of goal.
But the Greek crowd was abruptly silenced a minute later when Huntelaar fired in pass from Lewis Holtby.
Huntelaar missed a penalty in the 61st minute, striking the post.
"We kept our heads and that was the important thing — it won us the game," Schalke coach Huub Stevens said. "Even when they levelled, we stayed cool. So overall, I think the result was fair ... we went for it, and by the end of the game we could have had more goals."
Olympiakos defender Yiannis Maniatis said his team had to make "many improvements" before their next game against Arsenal in London next month. Arsenal won 2-1 at Montpellier on Tuesday to join Schalke at the top of Group B.
"We definitely could have done more. But we didn't take our chances," he said. "Their second goal came so quickly after ours and it really threw us off. We lost our concentration."