After a dour opening half hour, the evergreen Phillips nodded the Seasiders ahead from a corner, only for Beckford and David Nugent to respond with goals either side of half-time to put Leicester ahead.
Substitute Roman Bednar made it 2-2 with 21 minutes remaining, before another replacement, Leicester’s Ben Marshall, crossed for Beckford to head his second.
There was to be another twist in the tale, however, as Phillips popped up in stoppage-time with a close-range equaliser to boost his side’s play-off hopes.
The hosts were unchanged from their 3-1 victory over Brighton at the weekend, while Lee Peltier and Danny Drinkwater returned to Leicester’s starting line-up in place of Sol Bamba, who dropped to the bench, and the injured Paul Gallagher.
The opening 15 minutes were almost entirely devoid of incident, but Leicester gradually picked up the pace, Nugent forcing the game’s first save from Blackpool goalkeeper Matt Gilks.
The visiting supporters were left fuming soon after when Nugent went down in the box under Neal Eardley’s challenge, only to be shown a yellow card for simulation by referee Michael Naylor.
Blackpool’s threat going forward remained virtually non-existent as the half-hour mark passed, yet they then claimed the lead with their first meaningful attack.
Perhaps unsurprisingly, Phillips was the man to make the breakthrough, the veteran striker meeting Tom Ince’s deep corner from the right with a pinpoint header into the top-left corner.
Leicester wasted little time in drawing level through Beckford, who latched on to Drinkwater’s neat through-ball before sliding his shot past the onrushing Gilks.
There was then a noticeable lift in tempo when the two teams re-emerged for the second half.
After Beckford had threatened again for the Foxes, Blackpool were denied on three occasions as Kasper Schmeichel kept out efforts from Gary Taylor-Fletcher, Stephen Crainey and Eardley.
The goalkeeper’s trio of saves were soon given added value as Nugent headed home a Drinkwater corner to give his side the lead.
Leicester then wasted two golden chances to pull further clear. Danns blasted over from 10 yards after another Nugent header had been blocked and Lloyd Dyer was unable to convert Beckford’s low cross from the right.
After Phillips had missed the target with a header, Blackpool made their opponents pay for their profligacy. Bednar broke clear down the right and cut back inside Sean St Ledger before curling a left-footed shot beyond Schmeichel.
Leicester were back in front within four minutes, Beckford making no mistake in converting a pinpoint centre from Marshall, who had been on the pitch for little more than a minute.
Yet Blackpool were not finished and levelled again in dramatic fashion when Ince dribbled into the box before finding Phillips, who calmly stroked in his 17th of the season.