Three minutes in, the ball rebounded to Hazard in the box who beat Mat Ryan with an unerring finish.
On a day where Hazard shone, here are five things we learned.
On the heels of that familiar combination, 21-year-old substitute Charly Musonda gave a nod towards Chelsea's next generation when his fine lofted ball unleashed Moses for a first Premier League goal in 14 months.
Reigning Premier League champions Chelsea made four changes to the team that were held at home by Leicester in their last league outing.
Chelsea: Willy Caballero 8, Cesar Azpilicueta 7, Andreas Christensen 6, Antonio Rudiger 6, Victor Moses 7, Tiemoue Bakayoko 6, N'Golo Kante 6, Marcos Alonso 6, Willian 8, Eden Hazard 8, Michy Batshuayi 7.
Ezequiel Schelotto was also denied by a smart block from Caballero and the hosts were eventually made to pay for their wastefulness in front of goal as Hazard (77) added his second of the afternoon and Victor Moses (89) rounded off the scoring as Chelsea wrapped up all three points to move above Liverpool into third.
Firstly the wing-back chased a loose ball against Caballero, winning the challenge and knocking the ball past the Argentine before being brought down.More news: Trump doctor: President 'has incredibly good genes'
More news: Mikel Merino reveals how Newcastle will tackle the Premier League leaders
More news: Australian Open: Maria Sharapova's Victory Dreams Shattered By Angelique Kerber's Power Knock
Jamie Redknapp is unsure if VAR would have rectified the referee's decision not to award Brighton two penalties against Chelsea because it is a system based on "opinions and not facts". It's very hard for a referee to whistle for a penalty.
Wednesday's FA Cup penalty shoot-out win against Norwich City ended a run of four games without a win in all competitions for the Blues.
The Argentine had a handful of weak punches keep his side in danger and his passing was sub-par, completing just 11 of his 20 attempts.
While Chelsea were busy counting their goals Brighton and Hove Albion were counting their cautions as three of the players received yellow cards in the 36th, 56th and 79th minutes respectively.
The signing of striker Jurgen Locadia is promising, but the Dutchman will be required to hit the ground running following his switch from PSV.
After the break, Chelsea remained a threat on the counter but it was Brighton creating the clearer cut chances.
Chris Hughton had unexpectedly dropped winger Anthony Knockaert from the squad but the Seagulls' manager insisted he was unaware of reports the winger had left the stadium before the game.