Ao Tanaka's deflected shot put Leeds ahead after 32 minutes on Monday (Tuesday AEST), before man of the match Calvert-Lewin moved into top gear.
The big striker has a great record of scoring against Newcastle and had also hit the net in all of Leeds' past five home matches.
Calvert-Lewin was unlucky to see a 34th-minute header marked down as an own goal after brushing the head of teammate Jayden Bogle on the way in.
But there was no mistaking his authorship of the third, which squirmed under the keeper after he poked it goalwards under pressure from defenders.
"He is in outstanding shape and plays with confidence," Leeds coach Daniel Farke said of his No.9.
"I expect him to lead the group and he has taken that responsibility.
"I never doubt his goals, but it isn't just his goals, it is the way he plays for us. It is outstanding and he's one of the standout strikers in this league."
The Leeds forward line was helped by Newcastle's atrocious defending, and another weak clearance led to a fourth goal after 59 minutes, Noah Okafor slapping his low strike through a sea of legs into the far corner.
The only bright spot for the visitors came in the final minute when substitute Bazoumana Toure scored a consolation goal.
"That is football, that is the Premier League," said Newcastle coach Matthias Jaissle.
"You have to bring the fundamentals on the pitch, especially against a physical and intense team like Leeds.
"We couldn't match that physicality in the first half and that was a key element. I don't want to search for excuses now, we need to learn out of it and do better."
