Leicester struck after 25 minutes when the flying Japanese beat goalkeeper Rob Elliot from close range after striker Jamie Vardy nodded the ball across the danger area.
Claudio Ranieri's men have 63 points with eight matches to go, five ahead of second-placed Tottenham Hotspur, 11 in front of third-placed Arsenal and 12 ahead of Manchester City who both have a game in hand.
Leicester have been consistent all season, having now ground out 12 wins by a one-goal margin, more than any other team, and went about the task with the usual aim to put their opponents under pressure at the King Power Stadium.
However, they managed just one shot on target, albeit a special strike, against a battling Newcastle who remain second-bottom on 24 points, one behind Norwich City and north-east rivals Sunderland.
"Shinji works his socks off week-in, week-out so he deserves something like that. A special goal, a special moment for us," Leicester midfielder Danny Drinkwater told Sky Sports television.
"We got the goal and kind of sat back I think. It was pretty ugly on our side but it's the three points that matter."
Spaniard Benitez, who joined Newcastle on a three-year contract on Friday to replace the sacked Steve McClaren, having himself been fired by Real Madrid in January, could not have faced a much tougher opening fixture.
Leicester winger Marc Albrighton kept Newcastle's defence on their toes and it was from his cross that they scored.
Okazaki had it all to do when he received the ball with his back to goal but the Japanese guided the ball expertly into the corner.
"They (Leicester) are playing a very, very high tempo. It's not easy for any team. I was not happy (with the goal) because too many balls were bouncing around a lot," said Benitez.
Newcastle worked hard to get back into the match but did not create any clear-cut chances and Benitez now has an even bigger task on his hands to keep his side up with a crunch match at home to Sunderland, who are fourth from bottom, on Sunday.
(Writing by Ken Ferris; Editing by Tony Jimenez)
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