Two goals in the opening six minutes set up the win, with Hazard converting a deflected Victor Moses cross before Willian scored from Michy Batshuayi's flick in a brilliant team move.
Chelsea goalkeeper Willy Caballero, in for the njured Thibaut Courtois, withstood heavy pressure from Brighton, saving superbly from Tomer Hemed before seeing Davy Propper's header hit the post.
The visitors capitalised with Hazard's solo effort and a late fourth for Moses, following substitute Charly Musonda's lofted pass.
Chelsea move up to third with the win, while Brighton are 16th.
Brighton: 31 Jan v Southampton (A)
Chelsea: 31 Jan v AFC Bournemouth (H)