Robinson added to his treble at Huddersfield last month to help the Seagulls to their first FA Cup success since 2001 against their sorry Conference opponents.
Dean Cox launched the rout only after eight minutes. Goalkeeper Michels Kuipers released Tommy Fraser after catching a Northwich corner. He in turn found Dean Hammond who set Cox up for a right-foot curler.
Robinson launched his hat-trick after 18 minutes. Picking up possession from Hammond midway inside the Northwich half, he ran straight at the heart of the defence before finding the bottom corner with a right-foot drive from just inside the box.
Paul Brayson missed a great chance to put Northwich back into contention in first-half stoppage time when he sent a downward header wide from point-blank range.
Michael Carr also had a shot deflected against a post off a Brighton player early in the second half, but the visitors caved in once Robinson escaped from Gareth Griffiths close to the touchline to strike his second of the game in the 56th minute.
Alex Revell made it four, eight minutes later with a well-struck effort from 25 yards.
Robinson completed his hat-trick 11 minutes from time with another impressive finish, firing right-footed into the roof of the net from just inside the Northwich box.
Northwich were well and truly down and out by this stage but their agony wasn't over.
Joe Gatting, brought on in place of Revell, slotted his first senior goal on 82 minutes after Phil Senior made a one-handed save from Adam El-Abd.
Sam Rents also came on to score his first senior goal when Cox set him up on the stroke of full-time after he had taken over from Robinson.
Cox rounded off the massacre in stoppage time with his second of the game from Gatting's pass.