The teenage Brazilian had fired City ahead early in the first half only for Swansea to draw level through Gylfi Sigurdsson 10 minutes from time.
But in a dramatic finale, Jesus pounced to fire home a dramatic winner after his 92nd minute header had been saved by Swans keeper Lukas Fabianski to send the Etihad wild.
It was Jesus’s third goal in just two starts for City and his first goals at his new home ground.
And Jesus admitted it was an extra-special thrill to open his account at the Etihad as he produced a superb man-of-the match display for Pep Guardiola’s side.
“It means a lot especially in front of our fans - I’m very happy to score both goals,” the 19-year-old admitted afterwards.
“I’m happy to get into the team so quickly.
“Everyone has tried to help me. I have been able to settle in England very quickly thanks to my family and the Club and when things go like this it’s very, very good.
“I am really happy above all that we won. They scored to level but I think we deserved the win.”
