Lomano Lua Lua gave Blackpool the lead after 24 minutes with a strike from inside the area after good work from Martinez Angel.
Fleetwood improved after the goal and managed to frustrate Blackpool as they went in at half time only a goal behind.
The home side's good work was undone straight after the interval as Phillips scored the first of his goals with a strike from outside the box, leaving Scott Davies with no chance in the Fleetwood goal.
Thomas Ince extended the Championship side's lead ten minutes later with a smart finish into the top corner of the net.
Fleetwood's competitive edge was rewarded on 70 minutes as Jamie Vardy managed to pull a goal back.
Phillips then showed his class to score twice in the space of five minutes to complete his hattrick and send Blackpool easily into the fourth round.