City can now focus on preparing for Watford on Tuesday night while their rivals face hard matches on Sunday, with Liverpool playing Everton in the Merseyside derby while Arsenal and Tottenham meet in north London.
"In the second half one action from Raheem Sterling changed the game".
For his part, Guardiola praised Jesus' all-round contribution against Bournemouth and said he had no concerns that the Brazil international's goal drought would continue much longer.
"I don't know if Aguero will be fit".
There was certainly a late flourish, with David Silva coming off the substitutes to help inspire a classic third in tandem with man-of-the-match Leroy Sane, but this victory was more a triumph for perseverance than anything else after Callum Wilson had cancelled out Bernardo Silva's early goal.
Wilson's equaliser was reward for a Bournemouth team who finished the first half on top, and Guardiola admitted he struggled to find a solution until a mazy run from Sterling - which ended with his shot rebounding off the post - lifted City spirits eight minutes into the second half. "Sometimes it happens. It is a lesson we have to learn, how to win when we are exhausted".
"Before I came to City I was meant to be one of the best young players in the world; two months there and I was the worst thing going".
"It is another reality how the people attack our team, it's completely different here for the way they play".
Mourinho sat stern-faced on the bench as Southampton celebrated and his expression was even more vexed eight minutes later as Marcus Rashford's needless foul on Mario Lemina led to Southampton's second.
The Reds fell behind to an early Stuart Armstrong strike and when Cedric doubled Southampton's lead from an excellent free-kick the signs looked ominous.
If Saints fans were concerned about letting another two-goal lead slip like they did last week against Fulham, they were right to be anxious as United quickly hit back through Lukaku who was set up by Marcus Rashford.
Guardiola is not concerned about Gabriel Jesus' lack of goals and said his work ethic is helping the team as they try to defend their Premier League title.
Leicester City climbed to seventh in the table after James Maddison scored a fine individual effort to add to Jamie Vardy's opener from the spot in a 2-0 victory over Watford, who had Etienne Capoue sent off.