The Greek champions were arguably second best for long periods of the Group A clash at the Karaiskakis Stadium, but were rewarded for their clinical finishing.
Atleti will rue their profligacy in front of goal and coach Diego Simeone - who took a watching brief from the stands due to a touchline ban - must wonder how his side failed to take at least a point back to the Spanish capital.
The La Liga champions came agonisingly close to winning the Champions League in last season's final, as they held a 1-0 lead until the 93rd minute before going on to lose 4-1 to city rivals Real Madrid after extra time.
That European campaign saw Atleti go unbeaten in six away contests, but the visitors were two goals adrift by the 31st minute on Tuesday following Arthur Masuaku's driven effort, then on-loan Barcelona forward Ibrahim Afellay added a second with a composed finish.
Mario Mandzukic reduced the deficit before half-time, but Kostas Mitroglou, who returned to the club in the last transfer window after a short and unsuccessful spell at Fulham, slid home from close range to make it 3-1 after the break.
Antoine Griezmann enjoyed an impressive performance off the bench and he gave Atletic hope with a close-range finish in the closing stages, but his strike proved to be in vain.
There was an early break in play when Mandzukic received treatment after being caught on the nose by Pajtim Kasami's elbow.
Shortly after play resumed, Miranda was on hand to make a superb clearance from Kasami's teasing cross with Alejandro Dominguez lurking.
However, Atleti were caught off guard from the resulting set-piece and found themselves behind after 13 minutes.
A short corner was worked to Masuaku, who moved forward unchallenged from the left and drilled a 25-yard shot low into the far corner.
Seeking a swift response, Atleti peppered the Olympiacos box, with Mandzukic and Raul Garcia both heading chances wide.
Olympiacos soaked up the pressure and were rewarded with a second goal against the run of play shortly after the half-hour mark.
Dominguez showed great determination down the left before picking out Afellay, via a clever dummy from Mitroglou, and the forward made the most of miscommunication between Mario Suarez and Cristian Ansaldi to steer his shot past Oblak.
Atleti were back in the contest after 38 minutes, though, when Ansaldi's excellent delivery from the left was guided home by the head of Mandzukic from eight yards.
The visitors continued to ask questions of the Olympiacos defence after the break, but the hosts' rearguard dealt admirably the pressure.
Griezmann entered the fray for Atleti shortly before the hour-mark and the forward almost made an impact with a stinging effort towards the top right-hand corner which drew a fine save from Roberto.
The France international added a fresh impetus to Atleti's attack and soon after he broke clear down the left and once more forced Roberto into a great save low to his right.
Yet again, though, the hosts made Atleti pay for failing to take their chances in the 73rd minute.
Kasami drifted past Diego Godin on the right and found Mitroglou, who turned well and side-footed home from close range.
Griezmann offered hope of a late fightback when he tapped home Koke's fizzed cross in the 86th minute, but Olympiacos stoof firm all three points..
