Vardy found the net either side of Paul Dummett's own-goal, before Wilfred Ndidi struck late as Leicester claimed its fourth win from the last five league matches, losing only against Manchester United.
The Foxes are a contender to break into at least the top-six this season — with 14 points from seven games so far — and were ruthless against the only team to defeat them at home since Brendan Rodgers took charge in February.
American defender DeAndre Yedlin made his first appearance for Newcastle since April after undergoing groin surgery, coming on in the 74th minute. Leicester went ahead when Pereira played a one-two with Ayoze Perez — playing against his former club — and burst forward before side-footing the ball into the bottom corner.
Newcastle was reduced to 10 men with two minutes of the first half remaining. Midfielder Hayden was dismissed for a dangerous tackle on Dennis Praet, with the decision standing following a VAR check. Leicester made it 2-0 after 54 minutes. Praet sprayed the ball out wide to Harvey Barnes who cushioned a first-time pass over the top into the path of Vardy and he beat Martin Dubravka at his near post.
There was more misery for Newcastle shortly afterward when an attempted low cross from Praet was turned past his own goalkeeper by Dummett. Vardy grabbed his second of the game and Leicester's fourth after 64 minutes when he nodded home Marc Albrighton's cross from the left.
Ndidi wrapped up an impressive victory for Leicester with a smart shot on the turn in the last minute. Bruce called it a "bad, bad performance" with Newcastle in 19th place on five points. Manchester United hosts Arsenal on Monday to complete the seventh round.
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