The Gulls had reached the third round with victories over Chipstead, Evesham and Oxford United.
The home side looked to striker Tim Sills for inspiration as he scored both goals against Evesham, while Seasiders' caretaker boss Tony Parkes had to make do without a host of loan players who left the club this week.
The opening minutes at Plainmoor saw few openings at either end, with the Championship visitors giving little away in defence.
Ben Burgess and David Fox threatened for the Seasiders, but the home side were also holding firm at the back.
Torquay then hit the front just past the half-hour mark as Green took down a long ball forward from the back and placed an accurate left-foot shot past visiting keeper Paul Rachubka.
The Gulls held on to their advantage up to the interval, with boss Paul Buckle delighted with his side's efforts.
Soon after the restart, Sills put the Tangerines defence under threat a couple of times.
Stuart Green then headed wide from Danny Nardiello's cross just before the hour mark, as the Championship side upped the pace.
Midway through the second half, Sills was in the thick of the action again as he met a Kevin Nicholson free-kick, but couldn't direct his header on target from six yards out.
Blackpool threw on a couple of substitutes as time ticked away at a freezing cold Plainmoor, but in truth they failed to seriously test home keeper Scott Bevan in the closing stages.