Chelsea now find themselves level on points with fourth-placed Arsenal, while Brighton remain five points above the relegation zone after making little impact in West London.
The 18-year-old saw a curling effort deflected wide of the far post in the 11th minute, but Brighton looked sharp on the break with Solly March firing into the side-netting at the back post.
Chelsea upped the tempo as the first half progressed with Cesar Azpilicueta heading off target from a Hudson-Odoi cross, while Hazard directed a volley over the crossbar after the ball had fallen invitingly for him by the penalty spot.
Sarri's side eventually made their pressure count shortly before the break, with Hudson-Odoi delivering a low cross into the penalty area for Giroud to flick into the roof of the net at the near post.
Both sides showed plenty of attacking intent at the beginning of the second half, and Chelsea missed a chance to double their advantage when Hudson-Odoi somehow failed to nod past Mathew Ryan from close range after being picked out by Jorginho.
However, it was not long before the home side extended their lead. Jorginho and Loftus-Cheek linked up to present Hazard with an opportunity on the edge of the area, and the Belgian proceeded to curl the ball into the far corner from 20 yards out.
The goal put Chelsea in full control of the contest, and the three points were quickly wrapped up in some style as Loftus-Cheek went from provider to goalscorer by finding the top corner of Ryan's net from a similar position to Hazard's effort minutes earlier.
Sarri would have wanted his side to push hard for more goals given that goal difference could come into play at the end of the campaign, but only N'Golo Kante went close with a difficult volley from close range.
Anthony Knockaert also went close to netting a consolation for Brighton in the final stages having latched onto a long pass from Lewis Dunk, but the substitute sent a shot wide of the post after beating Arrizabalaga to the ball.
The goal would have been harsh on Chelsea who defended with authority all evening, and Sarri will be delighted that his side have been able to breeze through another 90 minutes given their current hectic schedule.
CHELSEA (4-3-3): Arrizabalaga; Azpilicueta (Zappacosta 73'), Christensen, David Luiz, Palmieri; Kante, Jorginho, Loftus-Cheek (Kovacic 82'); Hudson-Odoi, Giroud, Hazard (Willian 84')
BRIGHTON & HOVE ALBION (4-3-3): Ryan, Bruno, Duffy, Dunk, Bong; Propper, Stephens, Bissouma; March (Knockaert 31'), Andone (Murray 70'), Jahanbakhsh (Bernardo 75')