When Aguero's powerfully struck spot kick was turned away by the legs of Kasper Schmeichel in the 62nd minute, it meant City had missed its last four penalties in the league — and five out of seven this season.
Aguero was replaced by Jesus, who ran onto a pass from Riyad Mahrez following the former Leicester winger's surging run and slid home a finish for the 80th-minute winner. It was far from a scintillating display from Pep Guardiola's men, but they will take confidence from a solid performance away to a team one place below them in the table days before a trip to face Real Madrid in the last 16 of the Champions League.
City moved seven points ahead of third-placed Leicester and was 19 points behind leader Liverpool, but cannot qualify for next season's Champions League after receiving a two-year ban from European competitions last week for breaching UEFA's financial regulations. City has said it will appeal against the ban to the Court of Arbitration for Sport.
The big negative for City on the night was its inability to score from the spot, again. Leicester had two penalty shouts turned down before conceding one when Dennis Praet raised his right elbow and blocked a shot from Ilkay Gundogan. The penalty was awarded by VAR, Aguero went for power, but Schmeichel got down to his right and saved.
The previous three misses came from Raheem Sterling against Wolverhampton in December, Jesus against Sheffield United in January, and Gundogan at Tottenham this month. The match could have turned out very differently had Jamie Vardy not hit the post inside the opening 10 minutes for Leicester after slipping in behind City's defense.
Aymeric Laporte's return has been a major boost for City but the French defender was at fault when his sloppy pass gifted possession to Youri Tielemans, and his first-time ball allowed Vardy to get goal-side of Fernandinho.
As Ederson ran out, Vardy slipped the ball past him. Leicester manager Brendan Rodgers raised his arms in celebration on the sideline, but the ball struck the left-hand post and bounced back - to Vardy's disbelief.
City responded well as Mahrez tested Schmeichel before Gundogan failed to capitalise on a flowing move by shooting tamely at the goalkeeper. Leicester wanted a penalty when Kevin De Bruyne raised his hands to his face in the wall as James Maddison's free kick struck him, but referee Paul Tierney was not interested.
Another Maddison free kick brought a good save from Ederson before the City goalkeeper was at the heart of Leicester's second penalty claim moments later. The Brazilian clattered into Kelechi Iheanacho, flattening the Nigeria striker as he tried to meet Maddison's chipped pass -- but City's goalkeeper had just managed to beat the Leicester player to the ball. Iheanacho returned after lengthy treatment, but was replaced at halftime.
Leicester started the second half brightly but it was City which threatened as De Bruyne brought a fine save from Schmeichel with a drilled, low shot. Aguero's penalty miss inspired Leicester as the hosts ramped up the pressure at the other end, with Vardy flashing a powerful shot wide.
City was to make the decisive breakthrough, though, through Jesus after he replaced Aguero in the 77th minute. Mahrez drove forward, twisted and turned to leave Christian Fuchs wrong-footed, then played in Jesus, who made no mistake to slot the ball home at the near post.
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