Maurizio Sarri shuffled his pack from Sunday's contentious 2-1 win at Cardiff City, handing Hudson-Odoi his first league start in the process, and Chelsea rarely looked like dropping points as they produced an excellent display at Stamford Bridge.
Hudson-Odoi certainly made an impact out wide, setting up Giroud with a pinpoint cross to give the dominant Blues the lead just before half-time with his first Premier League goal since November.
Eden Hazard doubled their advantage with an hour played and Loftus-Cheek – who set up the Belgian – wrapped things up three minutes later with a gorgeous 25-yard strike, sending Chelsea above Manchester United and into fifth.
Hudson-Odoi was the first to threaten, as he cut in from the right in the 11th minute and saw his left-footed strike deflected narrowly over.
An even better opportunity fell to Hazard just after the half-hour mark, but he smashed a half-volley over from just inside the area when teed up perfectly by Giroud.
Chelsea did take the lead in the 38th minute, however, as Hudson-Odoi breezed past Anthony Knockaert and played a low cross towards the near post, where Giroud glanced a fine finish in with the outside of his foot.
Hazard increased the lead in the second half, receiving Loftus-Cheek's pass before committing Lewis Dunk and guiding a controlled finish into bottom-right corner from the edge of the area.
Loftus-Cheek went one better shortly after, his long-range effort curling into the top-right corner, leaving Mat Ryan helpless and completing a straightforward win.
Chelsea's depth highlighted before run-in
As the Premier League season enters its final stages, it can surely only be a good thing for Chelsea that their squad players look ready to rise to the occasion.
Hudson-Odoi, Giroud and Loftus-Cheek all impressed against Brighton, and that could be a timely boost in the race to finish in the top four.
