Maurizio Sarri’s men came into the game on the back of a fortunate victory at Cardiff and were aware that rivals Manchester United slipped up with a 2-1 defeat at Wolves on Tuesday.
Brighton remain on the fringes of the relegation battle, but came into the game no doubt with one eye on this weekend’s FA Cup semi-final clash against Wolves at Wembley.
And that is how it seemed as Chelsea dominated throughout with Olivier Giroud putting them ahead before half-time, while Eden Hazard and Ruben Loftus-Cheek wrapped up the points after the interval.
The win moves Chelsea above United into fifth spot, level on points with fourth-placed Arsenal, while Brighton remain in 15th spot – five points clear of the bottom three.
Chelsea boasted seven changes from their 2-1 win in Wales on Sunday with Callum Hudson-Odoi handed a first Premier League start, while Andreas Christensen, Emerson, N'Golo Kante, Loftus-Cheek, Hazard and Giroud also came in.
Gaetan Bong, Bruno, Solly March and Florin Andone all came into the Brighton side in four changes to the side which lost at home against Southampton.
The game took time to get going with the first attempt of note coming in the 11th minute when Hudson-Odoi was played in down the right of the area and watched as his effort was deflected over the crossbar off the boot of Shane Duffy.
Brighton’s first effort came just before the 20-minute mark when March met a Alireza Jahanbakhsh cross at the back post and smashed a volley into the side-netting with Andone waiting in the middle for the pull-back.
Hudson-Odoi then pitched a good cross into the area from the right on the half-hour, but Giroud watched as his close-range effort as blocked by a combination of Duffy and Bruno.
The visitors’ best chance of the half came on 35 minutes when Yves Bissouma did well to get the better of Cesar Azpilicueta down the left and then advanced into the area before he looked to tee up Duffy in the centre only for Andone to slide in and put his effort wide.
Hazard then spurned a golden chance to fire Chelsea in front, before the Blues got the opening goal their dominance warranted on 38 minutes.
Again Hudson-Odoi did the groundwork with some good play down the right before his low cross was met by Giroud who flicked the ball past Mat Ryan at the near post.
The second half followed a similar pattern with Chelsea dominating possession and after Hudson-Odoi sent a header into the arms of Ryan, the hosts doubled their lead on the hour.
Loftus-Cheek played a quick pass to Hazard on the edge of the area and checked inside before curling a wonderful strike beyond the dive of Ryan and into far corner of the net.
Loftus-Cheek got in on the act to make it 3-0 on 64 minutes when Hazard turned provider and the midfielder hit a brilliant strike into the net from around 20 yards.
Loftus-Cheek was inches away from making it 4-0 moments later and Kante then guided a shot over the bar after getting between two defenders to meet Hazard’s low cross on 70 minutes.
Brighton’s first attempt on target came in the 80th minute when a corner dropped to substitute Bernardo around 20 yards from goal but his strike was comfortably saved by Kepa Arrizabalaga.