The result meant that Chelsea will now face Bournemouth in the quarterfinal of the Carabao Cup while Derby's impressive run in the competition came to an end despite all the positives that were brought to light during the game.
Former Chelsea FC forward Zola, who is now working as Maurizio Sarri's assistant manager at Stamford Bridge, is confident Hazard is nearing a return to first-team action. Find out by following our live matchcast.
The size of the challenge to beat Chelsea was huge for Derby, with no win here since 1983 and no clean sheet since Peter Shilton's blank in 1987.
And with Lampard's record of taking Chelsea youngsters on loan - Mason Mount and Fikayo Tomori for example - Hudson-Odoi will be looking to impress.
Tom Huddlestone (Derby) Huddlestone plied his trade in the Premier League for many years, and on the basis of this performance the 31-year-old could still prove valuable for one of the smaller clubs in the division.
The Premier League giants moved into the EFL Cup quarter-finals after the tight win at Stamford Bridge on Wednesday.
Frank Lampard's men continued to be fearless with the ball at their feet and pulled the visitors back on equal terms yet again through Martyn Waghorn, who got on the end of a precise low cross from Mason Mount after Derby made full use of a momentary lapse in concentration from Chelsea following a throw-in.
Both Chelsea and Derby have enjoyed good starts under their new managers with the Blues now unbeaten in the Premier League and Derby sixth in the Championship.
Yet while Derby were obliging, they always carried a potent threat of their own with Mount and Harry Wilson pesky.
Injuries to Pedro and Eden Hazard leave Chelsea short on wingers.
Attention now turns back to league action this weekend and the manager wants his side to continue the good form built up.
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Ruben Loftus-Cheek should get a well-earned start having scored four goals in his last two appearances but Olivier Giroud is a doubt due to muscle fatigue so Alvaro Morata may keep his place up front.
Ruben Loftus-Cheek is now enjoying the best goalscoring spell of his career, netting in two consecutive games for the first time.
With rotation likely, Loftus-Cheek will be one of the favourites to start for Chelsea and could yet again find the net.
You'd have to go back to 2008 to find the last time the pair faced off at Stamford Bridge, a Premier League fixture.
The Championship side, conquerors of Manchester United in the previous round, provided a properly stern test of Chelsea's undefeated team in a thrilling game and were denied parity - and the possibility of another penalty shootout - only when David Nugent's late shot fizzed beyond Willy Caballero and rebounded back to the goalkeeper off the far post.