Badiashile made his first appearance since May after a long injury and turned in the first goal after a calamitous mistake from goalkeeper Leopold Wahlstedt.
Sterling added a second after Callum Brittain was caught in possession, curling a stunning finish in front of the Matthew Harding End.
Reece James made his first start since August in a crucial morale-boosting victory ahead of a trip to Tottenham on Monday.
Nizaar Kinsella was at Stamford Bridge to rate the Chelsea players...
Robert Sanchez - 6
Mostly comfortable but had his customary shaky moment with the ball. Claimed the clean sheet with an amazing last minute save on Arnor Sigurdsson.
Reece James - 7
The captain fired several long-range efforts on Leopold Wahlstedt's goal. Didn't seem at his absolute physical peak but still a dominating presence on the right.
Axel Disasi - 6
The man mountain dominated his duels but his positioning caught him out a few times. Reunited with his former Monaco teammate Badiashile for the first time at Chelsea.
Benoit Badiashile - 7
An impressive return to action after five months out, scoring from a simple side foot goal after a goalkeeping calamity.
Marc Cucurella - 6
Solid at the back but unremarkable when venturing forward.
Lesley Ugochukwu - 7
Made some good defensive interventions. It is clear Pochettino sees something in this young talent.
Enzo Fernandez - 8
An immaculate display returning after the birth of his baby boy. He is a £100million midfielder and looked like it against a lesser side.
Conor Gallagher - 6
Playing as a No10, he produced his usual high-energy display. Lucky not to concede a penalty.
Cole Palmer - 7
Hit the post and was involved in both goals but somehow not as dominant as he was in defeat against Brentford on Saturday.
Nicolas Jackson - 5
Held up the ball well but still not at his best, blazing over a good second half chance.
Raheem Sterling - 8
Again, looked like a player facing lesser opposition. Denied a stonewall penalty and had the beating of his defenders.
— Chelsea FC (@ChelseaFC) November 1, 2023
Malo Gusto - 7
Accomplished cameo helped control the match and came on in a planned substitution to rest James.
Levi Colwill - 7
Helped close out the final 30 minutes with ease, allowing Badiashile to rest in a planned change.
Moises Caicedo - 6
Helped bring a bit more control to midfield.
Alex Matos - N/A
Noni Madueke - N/A
Unused substitutes: Petrovic; Maatsen, Castledine, Washington