The Spanish outfit out had lost five of their last six in league and cup prior to Thursday night but goals from Pedro Rios, Jose Barkero and Obafemi Martins earned Juan Ignacio Martinez's men a notable scalp against a side who were playing in the Champions League group stages before Christmas.
It might have been even better for the European debutants but Martins missed a first-half penalty in an incident which saw visiting defender Djamel Abdoun sent off.
Olympiacos would have been in optimistic mood coming into the match after establishing a 15-point lead at the top of Super League standings with an away victory over nearest rivals Asteras Tripolis at the weekend, but they soon found themselves in deep trouble at the Ciutat de Valencia stadium.
There were just nine minutes on the clock when Levante took the lead through Rios, who latched on to Barkero's pass before sliding the ball past Balazs Megyeri, and 21 minutes later the visitors were reduced to 10 men when Abdoun was dismissed for bringing down Pedro Lopez inside the area.
The Greek giants survived the resulting penalty as Martins fired wide from 12 yards, but Levante did double their lead in the 40th minute after winning a second spot-kick.
Lopez was again the man impeded, Jose Holebas the guilty party on this occasion, but this time Barkero took over the penalty duties and he confidently fired past Megyeri to make it 2-0.
Levante's third goal arrived 10 minutes into the second half when Martins made amends for his penalty miss with a neat finish over Megyeri after latching on to another Barkero pass.
With their Europa League hopes threatening to go up in smoke, Olympiacos, who only just missed out on progressing through to the last 16 of the Champions League after finishing a point behind second-placed Arsenal in Group B, charged forward in the final 30 minutes in a bid to get a potentially crucial away goal ahead of next week's second leg.
However, Michel's men twice hit the woodwork, Kostas Manolas heading against the bar and Rafik Djebbour hitting the post, while Ljubomir Fejsa and Giannis Maniatis were both denied by Levante goalkeeper Keylor Navas as the home side held firm.
Levante also had chances to increase their lead in the closing stages, but despite not being able to beat Megyeri a fourth time, they will be delighted with their night's work.