Three goals in the opening 18 minutes of Sunday's game - a Wesley Hoedt own goal and finishes from Sergio Aguero and Davis Silva - put City in complete control before Danny Ings' penalty gave Southampton a lifeline.
Only Arsenal icon Thierry Henry and Manchester United legend Wayne Rooney had scored 150 league goals for the same club prior to Aguero's strike against the Saints.
Click on the video above to enjoy the best of the action from a memorable display at the Etihad...
"I can score a hat-trick so it was not the flawless day but we will take the three points", said Morata.
Sterling scored twice, taking him to 50 City goals, and added two assists to cap off a week in which he verbally agreed a new five-year deal with the reigning champions.
Southampton did pull a goal back through a Danny Ings penalty - the first City have conceded in the league since September 1 - but Raheem Sterling put any suggestion of a comeback to bed with a fourth in first-half stoppage time. "I spoke many times with Sergio".
Guardiola claimed the Sterling he encountered in his first season at City would look for excuses not to shoot but he believes the England forward is now going from strength to strength and, at 23, still has huge scope for improvement.
City, who now have a two-point lead over Liverpool, took just six minutes to open the scoring.
In truth, one of them probably should have just had a shot but you can't blame them for wanting to score the flawless goal.
"We played with the ball so good but not without the ball".
But City continued to threaten, and Sane nearly made it five with a vicious left-foot shot from the edge of the area that struck the bar just after the hour. He then added a fifth after the break and Sane made it six in stoppage time.