Derby are an ambitious club and can be a great platform for Lampard and co, but the onlooking Chelsea directors may dream of seeing one of the club's greatest players return to manage.
Fabregas got on the end of a cross from Davide Zappacosta, who had allegedly fouled Tom Lawrence in the build-up to it, to dispatch a fierce shot that hit Scott Carson on its way to the back of the net.
As reported by The Sun, Tomori was consoled by David Luiz, who had entered the fray as a substitute, with the Brazilian providing the youngster with some much-needed words of encouragement.
Derby lost 3-2 and was ultimately undone by two own-goals in the opening 21 minutes - the first of which was scored in the fifth minute by a player on loan from Chelsea, Mikayo Tomori.
Zola was unhappy with the way Chelsea finished the encounter, while he praised Frank Lampard's Derby. "I'm sure he'll be up for it and it will be important to get even more indications for us".
"Talking to the Chelsea players and some of their staff after the game, they were all praising us and saying how good we were".
Chelsea granted Derby special dispensation to field on loan pair Fikayo Tomori and Mason Mount against their parent club.
"That's probably the complaint I can make about them".
Chelsea's game against Derby County can be viewed by United Kingdom residents on Sky Sports Main Event and Sky Sports Football, which are channels 401 and 403 respectively on Sky and channels 501 and 503 respectively for Virgin Media users.
A stumbling Waghorn passed up a one-on-one chance to complete a quickfire turnaround and Derby punished themselves through more calamitous defending.
The only thing missing from Mount's performance was a goal - seeing a Lampard-esque effort from 25 yards deflect narrowly wide and another saved low down by Willy Caballero. Last time out, the Blues put on a strong XI to face Liverpool but could give Callum Hudson-Odoi his first start of the season as the games come thick and fast.
Chelsea have been drawn at home to Bournemouth in a repeat of last season's quarter-final. We are going to assess him tomorrow.
That's my goal. I want to come back and play for Chelsea, but at this moment I'm at Derby and I'm loving it, so that's where my focus is.
It will be the Blues' third match in the space of six days, having beaten BATE Borisov and Burnley in the Europa League and Premier League respectively.
Marriott has been directly involved in six goals in his past five games for Derby in all competitions (four goals, two assists).
But it failed to plug the leaks and it was no surprise that Fabregas forced home the third for Maurizio Sarri's side from close range in the 41st minute.