Catch Leicester's James Maddison on Soccer AM on Saturday.
Right after the midway point, Perez failed to take a first-time shot 76 minutes in after squeezing into the area, leaving Kasper Schmeichel to collect comfortably.
Perez was denied by a fine save from Schmeichel in a frantic finale.
Wilfred Ndidi and Youri Tielemans had long-range efforts after the break but the Foxes were struggling to create clear chances against a Newcastle defence sitting increasingly deep.More news: GOP College Group Apologizes for 'Domestic Terrorist' Email
But Newcastle had a nervy finale and Javier Manquillo was fortunate not to concede a penalty when he appeared to tug Tielemans' arm in the box in the closing stages.
The Spaniard put in a man of the match performance where he got the winning goal and put the Magpies on 38 points, 10 ahead of Cardiff.
Newcastle need reinforcements, but everything is up in the air at the moment because owner Mike Ashley is looking to sell the club for £400m, despite it being valued at £300m.
They should be assured of maintaining their top-flight status after a hard season tarnished by Benitez's discontent over a lack of backing in the transfer market from controversial owner Mike Ashley.More news: Trump considered nominating daughter Ivanka for head of World Bank
Leicester stayed in seventh place, tied on points with Wolverhampton Wanderers having played two games more. They have been brilliant since we came in and this has been the first real disappointment for them. His seven tackles were more than anyone else on the pitch recorded.
Leicester came into the match on a four-game winning run under recently hired manager Brendan Rodgers and had striker Jamie Vardy in superb form, with six goals in his last five league matches.
Perez's 32nd-minute header won the game with Newcastle claiming only their third away win of the season.
Ayoze Perez thinks that Newcastle are now safe from relegation after he scored the only goal against Leicester this evening.More news: Skype Preview adds screen sharing feature on iOS and Android
And Perez believes the result was the most important yet this season given that it has nearly certainly ensured another season of Premier League football on Tyneside.
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