The setback hardly knocked City out of their stride as they responded positively and were back ahead 10 minutes before the break as the outstanding De Bruyne whipped in a low ball from the right and Aguero flicked in from close range.
City appealed for a penalty when Rodri went down in the box under a challenge from Lamela but referee Michael Oliver gave nothing and VAR did not intervene.
The initial feeling behind the substitution was Guardiola being upset with Aguero's defending in the build up to Moura's goal, but that couldn't be any further from the truth as a frustrated Guardiola explained post-match.
"They have to fix it".
Sterling meanwhile also maintained his own superb start to the campaign thanks to his smartly-taken first-half header.
Roberto Firmino made it two with his 49th league goal for Liverpool, the Brazil forward taking Mane's pass, dribbling and then firing home in the 71st minute.
Liverpool's Sadio Mane inspired their win at Southampton.
QUIZ: How well do you know Liverpool's former Southampton players?
The incident took place in the second half as Liverpool led through Sadio Mane's fine opener in first-half stoppage time . The fan slipped as he was grabbed by a security guard and collided with several Liverpool players.
"Listen, after what happened against Tottenham when we scored in the 95th minute and more than 60,000 people were dancing and jumping and one second later we lost because it was offside, now I am used to these situations", he said.
Adrian ensured there was a nervy finish when he kicked a clearance straight at Southampton striker Danny Ings and saw the ball rebound into the net in the 83rd.
"We didn't get the three points, but that's the only thing we didn't get". There can be little debate about a ref performance and they now have no accountability again.
Sterling had given City the lead before Lamela equalised for the visitors.
On what was our 850th Premier League game, there was no shortage of drama with Pep Guardiola's side once more agonisingly denied by an injury-time VAR decision against the Londoners which ruled out Gabriel Jesus's injury-time strike.
"We worked together with an individual quality and capacity, but above all thinking like a team", said Emery.
Brighton and West Ham drew 1-1 in the other match.