Both sides had half-chances, with United inches from equalising late on and City doing what they do best - managing to take eight shots, four of which were on target.
City were forced to grind out the win, with United stopping City's silky attack following Jesus' ninth-minute opener.
Story of the match
Following Sheffield United's emphatic win in the red half of Manchester midweek, Chris Wilder's side looked to carry their momentum into a tough battle against the current Premier League leaders, Manchester City.
The side sat in 20th position deployed a very attacking line-up, with Rhian Brewster coming in for the Blades to lead the line along with Oliver Burke.
United's game plan was clear - sit back and attack City on the break. And this was almost utilised inside three minutes as a pacey Burke was played in behind. A brilliant sliding tackle from Ruben Dias mopped up for City, however, and the panic was over for now.
If there were any nerves coming into the game from the City players, they were quickly forgotten about as Torres was allowed to dance through two United players and pass the ball to Jesus in the six-yard box.
The Brazilian striker sat Aaron Ramsdale down, before firing home for his third goal of the campaign. Not only were City ahead inside 10 minutes, but Jesus had got the goal he was desperate for and his confidence seemed to be at a high.
Bernardo Silva will have been disappointed not to make it two as a disguised header back to the keeper was almost picked up by the Portuguese winger, but Ramsdale was happy to see the shot nestle in his arms and keep the score at 1-0.
United were growing into the game and making chances for themselves. The final ball just was not there for the Blades, however. Encouraging signs for the away side though.
A run from Torres, almost identical to his run for the opening goal, carved open the United defence on the 40-minute mark but his pass across to Jesus was cut out this time.
Sheffield United still had a fighting chance going in at the break, even with being a goal down. If they had any prospect of scoring, it seemed it would come through Burke and Brewster running in behind.
Opportunities to make City two to the good in the second half were identical to the first - thick and fast, but not taken.
There were worrying signs for Citizens as Phil Foden was checked over for concussion following a nasty collision with John Lundstram. City's top-scorer was able to continue, with many fans letting out a sigh of relief.
Jayden Bogle had, arguably, the best chance for Wilder's side as the wing-back latched onto an over-hit cross but blazed his effort into the stands behind Ederson.
A superb strike from Oleksandr Zinchenko stung the palms of Ramsdale as the Ukrainian bettered Bogle's previous effort from long range. The England keeper then kept Laporte out from the pursuing corner as the Frenchman rose highest above the United defenders.
John Fleck was inches from equalising at the Etihad with five minutes remaining. A rocket from the Scotsman had Ederson worried but was lucky to see the shot whistle past his left post.
Jesus must have thought he had closed the game out when fed through by Foden but Ramsdale was equal to the shot, to the amazement of the City striker.
The win for City meant, not only were they four points clear at the top of the league table before Manchester United play Arsenal, but Pep Guardiola recorded his 500th win as a manager.
Sheffield United were the underdogs in the game, but Wilder's team showed what more they had to give and that this season was not over yet. The Blades were going to fight until the very end.
Moment of the game
Jesus' goal for City was the only goal of the game, handing all three points to Guardiola's side.
City had to grind out a tough win against United, with the goal from the Brazilian coming inside 10 minutes.
The goal will do the young striker's confidence the world of good, after struggling to get into gear this season so far.