Raheem Sterling hit a hat-trick with Phil Foden also on target as City regained their 12-point lead over Liverpool.
After a draw with Burnley in midweek, United desperately needed a win at home to Southampton, but despite leading when Marcus Rashford put Jadon Sancho in the 21st minute they were again found destitute.
Southampton, beaten 9-0 on their final trip to Old Trafford, responded just three minutes after the break when Che Adams came on for a corner kick.
The visitors could win the match as Armando Borja forced David de Gea to save and Stuart Armstrong opened the scoring.
United have moved up to the fifth place, level on 40 points with West Ham United, but Arsenal (39) have two games in hand and Tottenham Hotspur (36) have played three of their last three games.
Everton secured their first league win under Frank Lampard to allay fears of relegation, beating Leeds United 3-0 to go five points ahead of third-placed Norwich from the ground.
Roy Hodgson's first home game against Watford went awry as a 2-0 home defeat by Brighton and Hove Albion left them in one spot under the table.
Brentford ended a five-game losing streak in the league with a 0-0 draw at home to Crystal Palace which is the only highlight coming before the start of the match as newcomer Christian Eriksen was introduced to the crowd eight months after suffering a heart attack at Euro 2020.
Sterling failed to score in his last five games. City however scored the winning goal against Norwich after 31 minutes on Carrow Road.
When Foden scored City's second in the 48th minute the result was a straightforward one but Sterling gave a shiny header and turned the rebound after his penalty was blocked by home goalkeeper Angus Gunn.
The city has now won 14 of their last 15 Premier League games, drawing one.
"We need more points. We know which opponent we have, the closest is Liverpool," said Guardiola, whose team has 63 of the 90 points he says he will need.
"(Liverpool) will not lose a lot of points because of the level they have. They are the best team they have had in the last ten years. We will have to win a lot of games."
While City motor is in full swing, United appear to be stuck under interim manager Ralf Rangnick who will soon make a decision on Cristiano Ronaldo.
The Portuguese has now failed to score in the last six games in all competitions - something he has not tolerated at the club level since January 2009.
"If he had wanted to score goals, I would have scored them," said Rangnick. "Today you got chances, one was off the line, and you had good times in the second half."
Also, not only Cristiano but as a team, we create enough chances but we can't score. It's a big problem.
"Everton's loss to Newcastle United in midweek left Lampard's side in a relegation battle. this week but I am very proud of the work, "Lampard said.
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