The Blues manager Frank Lampard shuffled the pack, with only Reece James, Mason Mount, Christian Pulisic and Tammy Abraham reamining from their defeat at Leicester City.
The hosts had a perfect start after Abraham opened the scoring in the 11th minute with a strike into the far bottom corner at the near post after Timo Werner raced towards goal from a quick throw-in and made a cut-back on the byline.
Abraham doubled Chelsea's lead six minutes later and grabbed his brace with a glancing header over goalkeeper Simon Sluga after a delicate cross by James.
Pulisic should have made it 3-0 for the Blues just before the half-hour mark after a dummy by Werner saw him go clear from a through ball on the left side of the box but his low shot was saved by Sluga.
Luton punished Chelsea immediately thereafter as Jordan Clark received a through ball at the back post and fired a strike past shot-stopper Kepa, who got a touch to the ball could not keep out.
Lampard's charges were putting the visitors under pressure in the closing phase of the first stanza, carving out chances but they were not clinical enough and they settled for a 2-1 lead going to the break.
Pulisic had a wonderful chance to make it 3-1 for the Blues four minutes from the break after a low cross by James but his first-time strike was saved by Sluga at the near post.
After creating plenty of chances, Abraham finally put the game to bed for Lampard's men and completed his hat-trick in the last quarter of an hour with a tap-in from close range after a square pass by Callum Hudson-Odoi, who had just come on.
Chelsea had a great chance to add a fourth goal in the last five minutes after they were awarded a penalty for a foul on Werner who could not capitalise, as his spot-kick was saved by Sluga, but the Blues were long out of sight, as they booked their spot in the fifth round with a comfortable 3-1 win.
