Vassilis Torosidis headed home Jaouad Zairi's cross in the 79th minute as Brazilian Zico, named as coach just hours before the match, watched from the stands while interim coach Bozidar Bandovic guided the Greek champions to a home victory.
Olympiakos, who parted company with coach Temuri Ketsbaia on the eve of the match, were missing some key players through injury and snatched the three points despite a lethargic display.
"I'm not that interested in the fact that I scored, I was more interested in us winning the game. The win will boost our morale," Torosidis told reporters.
"The last two months have been a bad period for us but it has been everybody's fault, not just the coach's.
"This will help our confidence but there are still five more games to go."
Alkmaar were making their group stage debut and coach Ronald Koeman said his team had suffered some big-stage nerves.
"Olympiakos were very good defensively and in the second half we didn't play well at all," he told reporters.
"My players were anxious because of their first appearance in the Champions League and at stadiums like this a team must gain experience for the future.
"I am very disappointed with the defeat. In the first half we had two good chances to score but we didn't take them."
CONSTANT THREAT
Both teams began cautiously, but the visitors had the first sight of goal when Moussa Dembele broke down the right and crossed for Maarten Martens, who somehow scooped the ball over from close range.
Torosidis crossed for Diogo as the hosts replied but the Brazilian forward was beaten to the ball by AZ defender Niklas Moisander.
The right flank looked the most likely source of a goal for the hosts with Zairi a constant threat.
Olympiakos should have been ahead after 55 minutes when Michal Zewlakow sent a low cross in from the right. Diogo cleverly left the ball for Dudu, who fired his shot over from inside the penalty area.
The visitors began to push forward as the match wore on with Australian midfielder Brett Holman probing down the left flank.
Holman cut inside after 72 minutes and drew a fine save from Antonis Nikopolidis with a powerful effort from distance but the former Greek international managed to parry the ball to safety.
Bandovic brought striker Kostas Mitroglou on with 15 minutes left to add attacking impetus and the hosts got the breakthrough with 11 minutes left when Torosidis headed home a teasing Zairi cross.
AZ threw everything they had in a desperate attempt to draw level in the closing stages and Nikopolidis produced a fine save to deny substitute Jeremain Lens. The hosts closed ranks as the clock ran down to hold on to a deserved victory.
