Patrick Bamford was the star of the show for Boro, opening the scoring in the fifth minute before winning the penalty that set up Grant Leadbitter’s second.
The second incident further hampered Derby, with Ryan Shotton shown a red card having been adjudged the last man.
Karanka, who served a touchline ban, said: “I think it’s the best afternoon of my career here. We played the best team in the league and are in a very good position in the table.
“It was a very good performance and I want to dedicate the victory to my staff because they are always with me.
“I could not be on the bench and they were brilliant once again.”
The big games come thick and fast for Middlesbrough, with a trip to promotion rivals Ipswich quickly on the horizon.
Karanka is fully aware expectations have been raised on Teesside, although he guarded against complacency.
He added: “I cannot manage the expectations outside the changing room. In the changing room, the expectations are the same. We are playing against teams that are around us in the coming weeks. Today was Derby, then we have Ipswich. We have four or five games now against teams towards the top of the table but it is important that we focus on each game.”
Middlesbrough: Konstantopoulos, Nsue, Ayala, Gibson, Friend, Adomah, Clayton, Leadbitter, Reach, Vossen (Wildschut 78), Bamford (Garcia 74). Unused substitutes: Husband, Whitehead, Omeruo, Veljkovic, Mejias.
Derby: Grant, Christie, Keogh, Shotton, Forsyth, Hendrick (Hughes 61), Mascarell (Ibe 46), Bryson, Russell, Martin, Dawkins (Best 46). Unused substitutes: Buxton, Coutts, Roos, Calero.
Referee: R East (Wiltshire).
Man of the match: Patrick Bamford.