Rafael Benítez wrote the script and Brendan Rodgers had no answer to it. This was a textbook away win for Newcastle and it means, barring a freakish series of results, that they will finish above the Premier League’s relegation places for a second season in a row.

Benítez aims higher than that and wants pledges of investment from the club’s owner, Mike Ashley, before committing his future to Newcastle. But here, at least, Benítez and his team celebrated a deserved win, sealed by Ayoze Pérez’s first-half header.

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Leicester remain seventh but their European ambitions were damaged by this defeat, which leaves them vulnerable to being overtaken by at least one of the clubs with matches in hand. Benítez said he is in talks with Ashley about making the sort of summer recruitment that would enable Newcastle to beat teams such as Leicester regularly enough to mount their own challenge for seventh place – although he would not accept that his team’s current tally of 38 points guarantees survival.

“We’re not safe yet, we’ll see what happens,” he said before explaining what he would like to happen in the summer. “Go into the transfer window and sign the players you need at the right time. The top six are a little bit far away but we can compete in the other range. We’re talking behind closed doors.”

This win was a perfect example of Benítez making the most of the resources available. It also presented Rodgers with a challenge that Leicester had not yet faced during their previous four matches, all won. Benítez suffered a blow last week in the form of Florian Lejeune’s season-ending injury but he persisted with a formation involving three centre-backs, with Paul Dummett filling in for the unfortunate Frenchman. Newcastle then executed their plan so well it was a wonder they had not won away in the league since before Christmas.

Facebook Twitter Pinterest Ayoze Pérez scores leaps to guide a superb header into the net for the winning goal. Photograph: Carl Recine/Action Images via Reuters

Both sides began briskly. In the first minute Newcastle forced a corner from which Jamaal Lascelles got off a header that Kasper Schmeichel had to block, albeit without difficulty. Within 20 seconds the action had switched to the other end, as Martin Dubravka stopped an effort from Jamie Vardy. Soon the contest settled into the expected pattern, Leicester probing while Newcastle strove to keep them at bay and strike on the counter, with Salomón Rondón serving as an ever-willing one-man front line.

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Rondón nearly opened the scoring in the 15th minute when he sent a terrific free-kick from 25 yards over the wall. Schmeichel could only wave at the ball as it flew past him. He was mightily relieved to see it bounce out off the crossbar.

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Leicester were struggling to pick a way through Newcastle’s defence, able only to fumble around the edges like men trying to retrieve a wallet from a prickly bush. But in the 21st minute Ben Chilwell cut through with a sharp one-two. Dubravka foiled his attempt to curl a shot into the bottom corner. Moments later the Slovakian thwarted Harvey Barnes, too. Then Newcastle tore forward and broke through. Matt Ritchie’s cross from the left was perfect and so too was Pérez’s run, which enabled him to beat Wes Morgan to the ball at the near post and guide a splendid header into the net.

By half-time Benítez’s plan was looking good and Rodgers needed to come up with a new one. Instead Leicester deteriorated as Newcastle chased a clinching goal. A cross from the left by Rondón offered Pérez a chance to double his tally in the 52nd minute but the Spaniard miskicked from 10 yards out. Fabian Schär then went on a safari downfield before setting up Miguel Almirón, whose attempted finish was wild.

Leicester were unable to feed Vardy for most of the match and then, when Youri Tielemans finally presented him with a chance, the striker shanked the ball into the stands.

“It was the first time I’ve seen us play in this type of game where the opponent sits deep with 11 men around the ball,” said Rodgers. “The important thing is to learn from it.”