Striker Okazaki won a forgettable game with an unforgettable first-half overhead kick as the Foxes maintained their grip on the Barclays Premier League with a 1-0 victory.
Tottenham’s 2-0 win at Aston Villa on Sunday had put Claudio Ranieri’s men under pressure but they won with minimum fuss, despite not being at their best at the King Power Stadium.
They go to Crystal Palace on Saturday after a five-game run which Ranieri had labelled as key to their chances, having won ten points from 12.
Defeat left Benitez knowing exactly what he needs to do to keep Newcastle up, with the Magpies a point below the safety line.
There was plenty of effort but the visitors were powderpuff when it mattered and their confidence waned as the game wore on.
They host drop rivals Sunderland on Sunday, in a crucial survival derby, and Benitez must demand more grit from his side.
He made two changes, with Aleksandar Mitrovic replacing Emmanuel Riviere while Vurnon Anita came in for the injured Paul Dummett.
The lack of options would have been alarming to the former Liverpool boss, with minimal switches from the abject 3-1 defeat by Bournemouth which cost Steve McClaren his job.
But there was plenty of fight by the Magpies in the opening exchanges as Ayoze Perez, Jack Colback and Moussa Sissoko went close in the first 15 minutes.
There was enough to give Benitez heart, but Leicester’s sluggish start was smashed in stunning fashion after 25 minutes.
Newcastle failed to clear Riyad Mahrez’s free-kick and, when Marc Albrighton sent the ball back in, Jamie Vardy headed across for Okazaki to execute the perfect overhead kick from six yards.
It was only the striker’s fifth league goal of the season but crucially settled an unremarkable game which could prove so key to both sides’ season.
Benitez retreated to the dugout and Albrighton nearly made it 2-0 two minutes later after a deep run ended with him curling inches wide.
Newcastle did not look like a team without confidence as they tried to probe the Foxes, but found little joy from Wes Morgan and Robert Huth.
A lack of creativity let the Magpies down, with Leicester not needed to be at their thrilling best to keep them at bay.
Perez shot straight at Kasper Schmeichel just before the break and Mitrovic struggled to justify Benitez’s faith when his 55th-minute header failed to trouble the goalkeeper.
The Magpies were still content to keep possession, with Leicester happy to let them, as the visitors turned to Andros Townsend in place of Anita.
Perez’s deflected drive whistled wide after 62 minutes but there was surprisingly little urgency by the Magpies as time ticked away and, with the hosts themselves struggling to create, the visitors never took advantage.
That will be a concern for Benitez and he was left frustrated when Mitrovic opted to pass to Siem De Jong rather than shoot with just six minutes left as Newcastle slipped to defeat.