Allen, 22, has been linked with a move to join former Swans boss Brendan Rodgers at Liverpool, and it is understood the Welsh club have already rejected an offer of £12.5million for the midfielder.
But the Wales international was in attendance, ahead of scheduled talks with new manager Michael Laudrup over the interest from Anfield.
Graham's treble, his first in Swansea colours, and an excellent finish from new signing Michu sealed Swansea's win while a Ludovic Sylvestre strike and Thomas Ince's penalty provided consolation for the Seasiders.
Laudrup could hardly have wished for a better start as Barry Ferguson's interception inadvertently teed up Graham for the striker to round Matt Gilks and net after just 43 seconds.
Graham was the provider for the second goal as a lovely exchange of passes allowed Michu to slot a composed left-footed finish.
Sylvestre rocked Michel Vorm's crossbar with a powerful drive but was not denied after 22 minutes when a sliced Ben Davies clearance allowed him to smash home a volley to pull a goal back.
However, Graham made it 3-1 right on half-time after Nathan Dyer seized on a poor pass and unselfishly squared for the striker.
Dyer also set-up Graham's third in the 64th minute after he raced past Ian Evatt and got a shot away which Gilks could only parry straight to the forward.
But the visitors had the last word as Ince netted from the spot late on.