Frank Lampard scored four goals as Chelsea put their FA Cup nightmare at Barnsley behind them to demolish Derby.
Scorer Lampard (right) is congratulated by Kalou and Ballack
Lampard slotted in a penalty after he was fouled by Dean Leacock, before Salomon Kalou knocked in the second.
Joe Cole crossed for Lampard to make it 3-0, Cole stroked home after Nicolas Anelka's shot was saved and Lampard sealed his hat-trick from 25 yards.
Lampard made it 6-0 with a left-foot finish inside the box before David Jones rolled in a Derby consolation.
The win leaves Chelsea five points behind Premier League leaders Arsenal with a game in hand on the Gunners.
Chelsea's fans seemed to be suffering an FA Cup hangover after their sensational quarter-final defeat on Saturday, with Stamford Bridge eerily quiet in the opening stages.
Lampard's early left-foot shot that rolled against a post threatened to liven up a low-key opening, but when Chelsea broke down Derby's defence just before the half-hour mark, the floodgates well and truly opened.
Leacock had come on for the injured Alan Stubbs early on and as Lampard broke into the box, the former Fulham defender upended him with an outstretched leg.
Lampard rolled the ball easily past Roy Carroll and from then on it was a question of how many the home side would score.
Three minutes before the break the lead doubled, Carroll racing off his line to thwart Anelka, but the ball falling to Kalou 25 yards out and the striker coolly sending the ball into the net.
Lampard took his tally to 17 for Chelsea this term with four goals
Carroll made an excellent save low to his left to keep out Kalou moments later but when play resumed after the break, Chelsea were rampant.
Lampard went on a mazy run that finished with a shot Joe Cole could not deflect on target, before Anelka headed a Kalou cross just wide.
But Chelsea were starting to make Derby look like a team with 10 points from 28 games and the Blues soon made it 3-0, Anelka playing in Joe Cole down the right, the winger getting to the byeline and crossing for Lampard to tap in from two yards.
The Derby that had battled for the first half an hour was a distant memory as Anelka raced clean through and after he saw his shot well saved by Carroll, Joe Cole followed up to slot into an empty net.
It kept getting worse for the visitors. Kalou cut in from the left, teed up Lampard and the England midfielder rifled a shot into the bottom right-hand corner via Carroll's right hand to complete his hat-trick.
He was not finished either, granted the freedom of the park to move infield after a one-two with Joe Cole and placing the ball into the near corner to wrong-foot Carroll and grab his fourth.
At 6-0 down, Derby finally managed a shot on target - and they scored with it. Miller's pass was deflected towards his own goal by Michael Essien and the ball fell kindly for Jones to beat Cudicini from close-range.
But the Rams have long been playing like a team already relegated and their effort will further have embarrassed manager Paul Jewell, now without a win in 19 games as boss.
Chelsea boss Avram Grant:
"I think we have a good chance to win the Premier League.
"If we win our game in hand we are two points behind Arsenal and they have to play here at Stamford Bridge still.
"Their games are not against easy teams - there are still 10 games to go, anything can happen."
Derby manager Paul Jewell:
"We are going to have to grit our teeth until next season now.
"The players tried their best, but as a group they just cannot compete with teams like these and this pace, they are playing at a different level to us.
"It is difficult to watch. It's a great league to be in if you are competitive, but there's no hiding place."
Chelsea: Cudicini, Ferreira, Carvalho, Terry, Ashley Cole, Ballack (Drogba 67), Makelele (Essien 73), Lampard, Joe Cole (Shevchenko 74), Anelka, Kalou.
Subs Not Used: Hilario, Alex.
Goals: Lampard 28 pen, Kalou 42, Lampard 57, Joe Cole 64, Lampard 66, 72.
Derby: Carroll, Edworthy, Stubbs (Leacock 16), Moore, McEveley, Sterjovski, Ghaly (Earnshaw 52), Savage, Pearson, Lewis (Jones 58), Miller.
Subs Not Used: Price, Villa.
Goals: Jones 73.
Ref: Chris Foy (Merseyside).
BBC Sport Player Rater man of the match: Chelsea's Frank Lampard 8.37 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.