Midfielder Craig Bryson scored Derby's first hat-trick against Forest since Steve Bloomer in the 5-0 victory in 1898, with Jeff Hendrick and Johnny Russell completing a day of misery for the visitors.
Derby had not scored in just over six hours but they were ahead after six minutes when Bryson beat Guy Moussi to a loose ball and drove a low shot past Karl Darlow.
It took Forest 30 minutes to have a shot on target but Derby found the net again twice in the space of five minutes to end the game as a contest.
Bryson went past Moussi too easily in the 32nd minute to convert Chris Martin's pass, and soon afterwards former Forest striker Patrick Bamford played in Hendrick on the left to slip the ball past Darlow.
Any hopes Forest had of staging a comeback were crushed in the 54th minute when Russell scored from 20 yards and Bryson completed his hat-trick from the penalty spot after Bamford was tripped by Darlow.
"We knew if we kept doing the right things the end product would come and there's no better day to do it than today in front of 33,000 fans." McClaren said.
"I think this win is for the Derby fans. We collect three points but for me, this is for the fans, they can have a great Saturday night, recover Sunday and probably do it again Sunday night and have a good day at work on Monday!
"So derby games are for the fans and we've collected three points, played very well and everything went today and our football got the goals.
"I think we got Nottingham Forest at a good time with all the injuries but I think this is the best win and probably the most satisfying purely because we kind of controlled the whole game."
McClaren also had words of consolation for his opposite number and former Derby boss Billy Davies.
"We had a chat in the tunnel," McClaren said. "You have to have humility in this game and he showed it at the end in our conversation. He was very humble and complimentary to our team."
Davies did not attend the post-match press conference for "legal reasons" connected to his appeal against a touchline ban, but his assistant David Kelly said: "Huge credit to Steve (McClaren) and his group, they thoroughly deserved the victory but we were disappointed in how we defended.
"It was a disappointing catalogue of goals we gave away and what we were working on during the week was disappointing in how it was executed on the day.
"But credit where credit is due, they took their opportunities and were very clinical.
"It's a huge, huge game in the season and we're disappointed we've let the fans down. We only had a fit group of 18 we brought today but that's not an excuse, it's just the facts of what's going on."
The result dealt a big blow to Forest's play-off ambitions but when asked if it puts Davies's job under threat, Kelly said: "You'll have to ask the chairman."