The visitors took a shock lead in the first minute through Andreas Lampropoulos but the advantage lasted just three minutes as Mitroglou levelled with his 11th league goal of the season.
The 23-year-old then took his tally to 12 with a simple header just after half-time to put his team 2-1 ahead before Jose Holebas added a third with a curling free kick.
OFI were reduced to 10 men after captain Christos Bourbos was dismissed after picking up a second yellow card with 15 minutes remaining and that provided the platform for two more home goals late on from Giannis Maniatis and Sambou Yatabare.
The win moved Olympiakos to 25 points, with PAOK snapping at their heels following an impressive 3-0 win at Panthrakikos.
PAOK, who have not won a league title since 1985, seem Olympiakos's strongest rivals for the title and Huub Stevens' team continued their relentless pursuit of the leaders thanks to two clinical strikes from Spanish midfielder Lucas Perez and an own goal from Pape M'Bow.
Panathinaikos, who have struggled for consistency in the early rounds of the season, are 11 points off the lead in fourth place after the Greens returned to winning ways with a 2-0 away success in Crete against Ergotelis on Saturday, taking their points total to 14 after nine games.
Late second half strikes from Luciano Figueroa and Giorgos Koutroubis secured three points for Yiannis Anastasiou's team, who were in desperate need of a boost after two successive defeats and with next week's home derby against Olympiakos approaching.