Lampard, who played 648 times for Chelsea and is the club's all-time leading goalscorer, was serenaded by home supporters during the match, and he was touched by the occasion, and also the performance of his players.
Instead of a foul Zappacosta took a quick throw-in and the late arriving Fabregas tucked in a few moments later.
On-loan Chelsea defender Fikayo Tomori missed his attempted clearance and watched in Halloween night horror as the ball ricocheted off his standing leg and deflected into the net to put the hosts ahead after five minutes.
The hosts had plenty of help due to two own goals from Derby players, but the victor was eventually scored by midfielder Cesc Fabregas just before half-time.
"We can call it a friendly draw, but Bournemouth is not going to be easy for sure".
Frank Lampard retains a huge place in Chelsea fans' hearts and his endlessly positive Derby County side will not be forgotten quickly by Chelsea either. "That's the complaint. But we'll go through this".
After twice equalising, the second time through Waghorn, Frank Lampard's side forced a number of good chances, notably through Jack Marriott and David Nugent, but were unfortunately denied.
It is pretty obvious that Derby securing loans from Chelsea for Mount and Tomori was due to Lampards connections to the club, but the former midfielder has proved it was not for kicks as his side have been impressive in the Championship so far.
"My players had to do really selfless stuff".
His side spent long periods of the game without the ball but they competed against the FA Cup holders, who are yet to taste defeat this season. The passing wasn't as sharp as it normally is, and the last 10-15 minutes we lost control. "That's why I try to just enjoy it and be up for it", he told Sky Sports. When you open up against a team with that quality, it is 50-50.
"My overriding feeling is thanks to the Chelsea fans and the Derby fans and pride at the team". "I did leave here quietly (in 2014), slightly out of the back door, so it's good to walk through the front door and get that". I turned round thinking we'd got the foul, then looked back and they were in our box.
Chelsea have now won 11 of their past 12 home games against Derby in all competitions, netting 37 goals in those matches (3.1 per game).
Substitute David Nugent struck a post in the 89th minute as Derby came close to a third equaliser, but Chelsea survived and progressed.
Fabregas has had a hand in seven goals in his past seven League Cup appearances for Chelsea (three goals, four assists).