The 20-year-old, who has now scored seven in four after returning from a successful loan spell at Sheffield United earlier this season, seized control late on after Micky Mellon's men had briefly threatened to make the headlines.
The non-league side were desperately unlucky not to reach half-time on level terms after dominating much of the first period and being denied by four superb saves by stand-in Blackpool keeper Mark Howard.
And Blackpool also had to thank Howard for another fine stop in the second half after Fleetwood hot shot Jamie Vardy reduced the deficit and threatened to make it an anxious last half hour for Ian Holloway's men.
Holloway had made his intentions clear by making only four changes for his side's journey eight miles up the Fylde coast tram tracks to face a Fleetwood side whose main goal this season is promotion to the Football League.
The visitors soon settled in their cramped surroundings, Phillips forcing a save out of Fleetwood keeper Scott Davies in the 18th minute before the hugely impressive Vardy headed just over from a Peter Till cross.
Blackpool responded by snatching the lead in the 24th minute when Lomana Lua Lua latched onto a through-ball from Bob Harris before chipping a delightful opener over advancing keeper Davies.
But if the opener was designed to quash Fleetwood's enthusiasm for an FA Cup upset it had the opposite effect as the home side poured forward and could count themselves desperately unfortunate not to claw back level.
Tangerines keeper Howard pulled off a superb double save in the 27th minute to deny first Vardy, who had drilled a low shot goalwards, and Till whose header from the rebound was tipped over the bar.
And five minutes later Howard pulled off more heroics when he parried a drive from Andrew Mangan before clinging onto a deflected shot from Vardy from the resulting corner.
Blackpool almost stretched their lead in first-half injury-time when a shot from Tom Ince was parried by Davies, and Phillips' follow-up was blocked by Fleetwood captain Steve McNulty.
Phillips' curling effort into the top corner inside two minutes of the restart appeared to have killed off Fleetwood's hopes of the second half revival, but Mellon's men kept pressing and Varney flashed a header onto the roof of the net.
Ince swept home Blackpool's third from a right-wing cross by Neil Eardley in the 55th minute but the hosts were still not spent and got their reward in the 70th minute when the dangerous Varney fired home.
The striker, whose 15 goals in 17 games to date this season have had some of Blackpool's Championship rivals interested, stole into the left side of the box and struck low past Howard.
Vardy briefly threatened to haul Fleetwood back into the game with another swinging left-foot effort from a Mangan corner two minutes later, which Howard once again saved superbly.
Phillips hit the post from long range in the 75th minute before wrapping the game up with a late solo show, knocking in his second on 77 after Lua Lua's initial effort was blocked, and completing his hat-trick nine minutes from time.