The Spanish striker made his decisive contribution with four minutes to go, poking the ball into his own net as he tried to prevent Shinji Okazaki scoring.
The Foxes had made a terrible start as their hosts – roared on by a vocal home crowd following pre-game celebrations to mark the club’s 125th anniversary – took the lead in the sixth minute courtesy of Joselu’s close-range finish.
The visitors rallied quickly and restored parity when Mikel Merino’s loose pass gave them possession and began an attack that Riyad Mahrez ended with a superb 25-yard, left-footed drive into the top corner.
Demarai Gray put them in front after the break with a shot that found the net via a deflection off Florian Lejeune before Dwight Gayle levelled matters with a shot that came off Harry Maguire, but City would have the final word.
It was an excellent victory for Claude Puel’s side, who have now earned 17 points from eight league games since Craig Shakespeare was sacked in October – a run of form that has taken them up to ninth.
Newcastle, meanwhile, have taken just one point from their past seven matches and the cushion between them and the relegation zone is just two points.
Defeat also represents the first time boss Rafa Benitez – who has previously managed Liverpool and Chelsea – has suffered three straight Premier League losses.
When Puel was appointed by Leicester, the team were 14th in the Premier League with just two wins from nine games.
The Frenchman had his doubters, who pointed – somewhat unfairly – to the 2016-17 season he spent in charge of Southampton, who he led to an eighth-placed finish and the EFL Cup final, but was accused of producing uninspiring football.
City’s seven games under him have yielded both points and goals, with their only defeat at the hands of league leaders Manchester City.
On Saturday they recovered from two setbacks – one early in the game, one late – and played the more cohesive, attacking football of the two sides en route to a reward they deserved for their 63% possession and greater number of efforts on goal.
In Mahrez, Gray and Jamie Vardy they have an incisive attacking trio who will trouble any defence in the league and one seemingly restored to their potent best by their new boss.
Mahrez has been directly involved in eight goals in 16 appearances in the Premier League this season (four goals and four assists), which is just one fewer than in 36 games last season, when he managed six goals and three assists.
Gray has netted three goals in seven Premier League appearances since Puel took charge, having scored just once in his first 50 games in the competition.
Vardy was unfortunate not to add to his tally – which now stands at seven goals in 14 league games – but it was he who provided the cross towards Okazaki that forced Perez into his game-deciding error.
