The two teams began the night with identical unbeaten starts to the PL campaign (W1, D2), but Leeds led from the start and should have taken a 14th-minute lead when wing-back Jayden Bogle produced a clever effort on the turn, only for Lukas Hornicek to tip it away brilliantly.
Bogle had scored in the Whites’ previous PL game, a 1-1 draw at Brighton, and he went close again 11 minutes later when his fierce effort was parried by the Newcastle goalkeeper.
However, Horníček was helpless for Leeds’ opener in the 32nd minute, as Ao Tanaka’s shot from the edge of the box hit Sean Steur and Lewis Miley before looping up and nestling in the bottom corner, which saw the latter credited with the own goal.
The hosts doubled the lead two minutes later when Calvert-Lewin climbed high to head home James Justin’s cross, with Bogle awarded the goal after the ball skimmed off his head.
The striker should then have scored when Hornicek parried a cross into his path, but the Czech made an excellent reflex save, shortly before Tarik Muharemovic produced a goal-saving block to deny Harvey Barnes at the other end.
Calvert-Lewin got the goal he deserved in first-half stoppage time, bundling his way past Sven Botman and firing low into the net to score his third goal in his last four matches across all competitions.
Lewis Hall tested James Trafford early in the second half, before Newcastle received a let-off when Anton Stach found the side netting after Botman gave the ball away.
The fourth goal arrived just before the hour mark, though, as Noah Okafor – who played under Magpies boss Matthias Jaissle at Red Bull Salzburg – piled the misery on his former manager with a half-volley from the edge of the box to open his account for the season.
The home fans were buoyant, while there was barely a murmur from the visiting supporters when Bazoumana Toure slotted home a consolation goal – his first in the PL – in the 90th minute.
The hosts’ victory moves them third in the fledgling PL table after going unbeaten in the opening four games of a top-flight season for the first time since 2001/02, while they have now lost just one of their past 13 league outings (W6, D6).
Meanwhile, Jaissle’s unbeaten start as Magpies boss is over, as Newcastle’s six-match run without defeat against Leeds ends in emphatic style.
Flashscore Man of the Match: Dominic Calvert-Lewin (Leeds United)