Gabriel Martinelli was Arsenal’s winning goal at the King Power Stadium in a game dominated by the visitors.
“For the amount of time we dominated possession of the ball, the territory and the number of situations we had in the last third, we should have created a lot more and scored more goals,” Arsenal manager Mikel Arteta said.
“When you don’t, you have to be exceptional at your defensive work and we gave up a shot. Defensively we were outstanding.”
Arteta’s decision to start both Martinelli and Leandro Trossard in the top three at the expense of Eddie Nketiah paid dividends.
Trossard had a brilliant shot into the top corner in the first half that was controversially ruled out by a VAR review for a foul by Ben White on Leicester goalkeeper Danny Ward.
But Martinelli could not be denied a minute in the second half when he coolly scored a pass from Trossard.
Bukayo Saka had a second goal disallowed for offside as Arsenal failed to turn their dominance into a more convincing score.
City had also been guilty of a lack of cruelty in front of goal in the 1-1 draws with Nottingham Forest and RB Leipzig last week.
But the defending champions put Bournemouth on the sword to reduce the gap at the top to two points.
Julian Alvarez, Erling Haaland and Phil Foden scored for Pep Guardiola’s men before halftime.
Álvarez’s shot was then converted into his own net by Chris Mepham early in the second half.
But City are now six games without a clean sheet as Jefferson Lerma netted a consolation for the Cherries, who drop to the relegation zone.
Liverpool could not make amends for their 5-2 thrashing at the hands of Real Madrid in midweek in a poor 0-0 draw at Crystal Palace.
The Reds’ chances of reaching the Champions League next season look slim as they remain six points behind fourth-placed Tottenham.
Mohamed Salah hit the crossbar in the second half for Jurgen Klopp’s men, who sit seventh in the table with one point.
Leeds had not won a league game since before the World Cup break, a run in which Jesse Marsch was sacked.
But they broke that run by beating Southampton 1-0 in a bottom-two clash before kick-off at Elland Road.
Junior Firpo scored the only goal 13 minutes from time to knock Leeds out of the bottom three.
“The club needed him after 10 games without a win,” Leeds manager Javi Gracia said after his first game in charge.
I am very happy for everyone who works at the club, the fans and especially the players because they were working without rewards.
West Ham were the other big winners of the day in the battle to overcome the drop, as four goals in the last 20 minutes potentially saved David Moyes’ place in a 4-0 win over Nottingham Forest.
According to reports this week, the former Manchester United manager was facing sacking if the Hammers lost.
Two goals in three minutes from Danny Ings transformed the atmosphere at London Stadium before Declan Rice and Michail Antonio sealed West Ham’s second league win since October.
Everton slipped back into the relegation zone after losing 2-0 at home to Aston Villa.
Ollie Watkins’ penalty and Emi Buendía’s goal condemned Sean Dyche to his first home defeat since taking charge of the Toffees.