Ilkay Gundogan put the result beyond doubt when the German finished a fine move involving Bernardo Silva and Sane in the 79th minute.
"In the first half it was flat, a lack of rhythm".
Among the goals in that streak was a victor seven minutes into injury time at Bournemouth in the third game of the last season.
Bournemouth suffered its sixth loss of the season and provisionally holds the ninth spot with 20 points.
At least one of their close contenders will lose ground with Arsenal and Tottenham meeting in the North London derby, although Guardiola said they should expect second-placed Liverpool to beat city rivals Everton.
That should have been United's cue to press home their momentum after the break.
"The good players, they would move for that experience, now maybe they feel after Sheikh Mansour took over they said, "We can win titles here" and they are comfortable with their families in the city and that's why they decide to stay, so it's simple".
"We haven't been outplayed for many moments of the game. It's just the key moments where we haven't been clinical".
Liverpool striker Origi reveals Klopp chat before substitution
That is the positive we have to take. "So it was always in my mind about Div that night (against Everton )". It was a lucky day for him this afternoon. "We are not children any more, that we celebrate for five days".
He claimed his attempt to improve the players against Bournemouth with a half-time team-talk did not work as well as he would have liked, and was grateful to Sterling for making the difference in the second half.
PEP WATCH - Is this the face of a man anxious about losing his Premier League undefeated streak?
Wilson was unable to make significant contact with Joshua King's cross, but City did not heed the let-off as the newly-capped England striker powered home a header from Simon Francis' ball into the box. Personally I would prefer us to run away with the League and open up a relaxing cushion of points.
"We are just in December but I have the same feeling as with Raheem - he can do better".
"The doctors told me [on Friday] Sergio can not play", Guardiola said.
Man City team news: How will City line up vs Watford?
Pep's side has been irresistible thus far in the Premier League but could have a tough time in Hertfordshire when they take on a Watford side who have shown glimpses of quality this season.
Newcastle's three-match winning run was abruptly halted as a goal in either half from Javier Hernandez and Felipe Anderson's injury-time strike gave West Ham a comprehensive 3-0 win at St James' Park.