The Brazilian opened the scoring after four minutes, tapping in from Oleksandr Zinchenko's cross, before doubling the lead by heading in Kevin de Bruyne's perfect delivery.
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Jesus then set up Rodrigo's superb long-range strike before netting his first Premier League hat-trick, coolly slotting in from the penalty spot after the interval.
The 25-year-old rounded off his superb display by adding a fourth, stroking in from De Bruyne's cutback. The attacker admitted his delight after a wonderful afternoon.
"Today was my day," he said. "We played very good today, we created a lot of chances, that's what we need to do.
"We made passes and passes to create chances and try to score, and today we were very good on the finishing.
"It was my first hat-trick in the Premier League. I've tried. Sometimes I've scored two then I've hit a post, the defender has blocked [my shot], or the keeper has saved, but today was my day.
"I'm very happy with the three points. The team played so good and we deserved it."
The Man of the Match also reserved some praise for teammate De Bruyne, who assisted him twice during the comfortable victory.
"He's an amazing player," he admitted. "Always trying to put the ball in the box. When I'm playing on the right side I do as well, but he does it better than me of course.
"Always when he has the ball I try to go in the area to finish and today I was happy he gave a very good cross and I could head it in."
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The victory takes Pep Guardiola's side four points clear at the top of the league, with second-placed Liverpool set to face Everton on Sunday. Jesus had reiterated that City need to simply focus on our own results for the remainder of the season.
"We have to do our job, not look to them. We know they have a lot of amazing players and can win all the games.
"We are in front and, of course, it's not easy but we have to do our job."