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 at the end of the five-game run which Ranieri had labelled as key to their chances, having won 10 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 as 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 to Bournemouth which cost Steve McClaren his job.
But there was plenty of fight from 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' seasons.
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 keeper.
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 from the Magpies as time ticked away and, with the hosts struggling to create themselves, 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.
Rafael Benitez took charge of Newcastle for the first time in their 1-0 defeat at Leicester on Monday after replacing Steve McClaren last week.
The Magpies are second bottom in the Barclays Premier League and a point from safety and, here, we look at how Benitez fared in his opening game.
All eyes were on Benitez's first selection as Aleksandar Mitrovic started with the boss suggesting the striker was included from the off to boost his confidence. The injured Paul Dummett dropped out along with Emmanuel Riviere, who was benched, as Vurnon Anita also returned. That there were only two changes from the abject 3-1 defeat to Bournemouth which cost Steve McClaren his job showed the lack of options and depth Benitez has to work with.
Ayoze Perez started on the right wing as Jack Colback was shunted to left back and Benitez hinted before the game Newcastle would go back to basics to find a result. The Magpies' high tempo start left Leicester ragged but they lacked quality to make it count and test Kasper Schmeichel. Newcastle had plenty of possession but struggled to use it well enough and while they were generally organised they failed when it mattered.
Benitez was perched on the edge of his technical area and directed every player with a calm aura rather than bark instructions at his new side. Claudio Ranieri looked the more agitated manager in the hosts' dugout as Benitez kept his cool throughout. The Spaniard showed little reaction to the final whistle and keeping calm during Newcastle's crucial relegation run-in will be crucial.
After just three days in the job there are always questions over exactly how much influence a manager could have. Newcastle started brightly, as expected in front of a new boss, but began to wilt once Shinji Okazaki opened the scoring. The Magpies did not look like a side who were second bottom and were generally composed on the ball but Benitez could not get the win he was looking for.
Benitez will now know the size of the job, despite having only replaced McClaren before the weekend. With a game in hand over Norwich and sitting just a point behind Sunderland - who they face on Sunday - all hope is not lost for the Magpies.
Benitez would have taken encouragement from elements of Newcastle's performance, if not their finishing, to know they can still survive.
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