Leonardo Ulloa headed the Foxes ahead after 38 seconds and it was 2-0 within 17 minutes as Wes Morgan poked home.
The visitors sealed the game early in the second half when Ulloa scored a penalty after Emmanuel Riviere shoved Marcin Wasilewski.
Both managers were in the headlines before the game for off-field arguments.
Leicester boss Nigel Pearson called a journalist an “ostrich”, “stupid” and “daft”during a bizarre post-match news conference following Wednesday’s defeat by Chelsea.
His opposite number, John Carver, asked his club for protection from their own fans and then invited two supporters around for a “cup of tea” after a heated exchange.
But there is no comparison between the two on current form.
Leicester were seven points adrift of safety at the start of April, but have now won four of their last five to move four points clear of the bottom three – for two hours at least.
Newcastle on the other hand were in the top half when manager Alan Pardew left for Crystal Palace at the turn of the year.
Carver, who was placed in charge until the end of the season after a caretaker spell, has overseen a scarcely believable decline in form. The Magpies have lost 12 of his 17 games in charge in all competitions.
If they stay up, it will be down to their results before Christmas as they do not look like a team capable of picking up another point.
They started off in disastrous circumstances as Marc Albrighton put in a corner which Ulloa headed home for the fifth quickest Premier League goal of the season.
It was game over by the 17th minute when Albrighton’s free-kick was converted by Morgan after Ulloa failed to get his own leg to it.
The second half started just as badly for Newcastle as the first when Riviere shoved Wasilewski in the back and Ulloa scored his second from the spot.
If Newcastle thought their day could not get worse, they were wrong. Williamson was sent off in the 62nd minute as he fouled Jamie Vardy for a second booking. And in injury time Janmaat did the exact same thing.
That means two of Newcastle’s first-choice back four will be suspended for next Saturday’s game against West Brom.
Leicester boss Nigel Pearson: “From the kick-off we didn’t allow Newcastle to feel their way in to the game. To get two goals in a short amount of time helped.
“With a couple of months to go our season was in danger of not happening as we’d like. But we’ve kept our destiny in our hands. Goal difference will be important – days like today help.
“Someone of John Carver’s integrity has to try to find solutions that are proving difficult to solve. I feel for him – he cares so much about the club. You’ve got a better chance if you have people who have a feel for the club. They still have more points than us. They’ve still got work to do but so do we.”
- 01 Schmeichel
- 27 Wasilewski (de Laet – 68′ )
- 14 Huth
- 05 Morgan
- 11 Albrighton
- 08 James Booked
- 19 Cambiasso (Hammond – 74′ )
- 15 Schlupp
- 26 Mahrez
- 09 Vardy
- 23 Ulloa (Kramaric – 78′ )
- 02 de Laet
- 03 Konchesky
- 04 Drinkwater
- 07 Hammond
- 32 Schwarzer
- 39 Wood
- 40 Kramaric
- 01 Krul
- 22 Janmaat Dismissed after an earlier booking
- 06 Williamson Dismissed after an earlier booking
- 02 Coloccini
- 36 Dummett Booked
- 14 Colback
- 04 Taylor (de Jong – 58′ )
- 18 Gutiérrez Booked
- 07 Sissoko
- 17 Pérez (Armstrong – 74′ )
- 29 Riviere (Anita – 64′ )
- 08 Anita
- 10 de Jong
- 20 Cabella
- 28 Ameobi
- 30 Abeid
- 32 Armstrong
- 41 Woodman
Live Text Commentary
Full TimeMatch ends, Leicester City 3, Newcastle United 0.
Full TimeSecond Half ends, Leicester City 3, Newcastle United 0.
90:00+2:24Attempt missed. Jamie Vardy (Leicester City) header from very close range is close, but misses the top right corner. Assisted by Riyad Mahrez with a cross.
90:00+1:31Attempt missed. Dean Hammond (Leicester City) right footed shot from outside the box misses to the left.
DismissalSecond yellow card to Daryl Janmaat (Newcastle United) for a bad foul.
90:00+0:10Foul by Daryl Janmaat (Newcastle United).
90:00+0:10Jamie Vardy (Leicester City) wins a free kick on the left wing.
89:10Offside, Leicester City. Ritchie de Laet tries a through ball, but Andrej Kramaric is caught offside.
87:54Corner, Newcastle United. Conceded by Kasper Schmeichel.
87:52Attempt missed. Siem de Jong (Newcastle United) right footed shot from the right side of the box is close, but misses to the right. Assisted by Adam Armstrong.
87:17Jack Colback (Newcastle United) wins a free kick in the defensive half.
87:17Foul by Riyad Mahrez (Leicester City).
86:44Corner, Leicester City. Conceded by Paul Dummett.
86:31Delay over. They are ready to continue.
85:25Delay in match Jamie Vardy (Leicester City) because of an injury.
84:52Foul by Moussa Sissoko (Newcastle United).
84:52Ritchie de Laet (Leicester City) wins a free kick in the attacking half.
80:22Foul by Paul Dummett (Newcastle United).
80:22Jamie Vardy (Leicester City) wins a free kick in the attacking half.
78:47Foul by Jack Colback (Newcastle United).