The hosts took the lead in the 38th minute when Mirallas slotted past Dario Kresic. PAOK rallied after half-time but any hopes of a comeback were extinguished when midfielder Vladan Ivic was dismissed after a second booking in the 58th minute.
Belgian forward Mirallas then smashed home a second from Dennis Rommedahl's lay-off and Rommedahl added a third with four minutes left.
The win moved Olympiakos, who have a game in hand, level on 24 points with Panathinaikos, but the Greens stay top thanks to their superior head-to-head record.
Panathinaikos had moved three points clear following their 4-2 home win over Iraklis on Saturday.
With new coach Jesualdo Ferreira watching from the stands, Panathinaikos fell 2-0 behind after just 21 minutes but roared back to clinch victory helped by two goals from Djibril Cisse.
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