City were nine points adrift of leaders Arsenal as they trailed Liverpool at Anfield following Dominik Szoboszlai’s stunning free-kick.
However, after goals from Erling Haaland and Bernardo Silva, City made a comeback in the final minutes of the game to secure a crucial 3 points.
The victory now puts City six points behind Arsenal ahead of the midweek fixtures, which Keane says should worry The Gunners who beat Sunderland 3-0 at the weekend.
"Big lift for City. Their record here is not great.
"Pep said before the game when you come to Anfield you need to show personality and character - and this City team showed it. Particularly in the second half.
"They were very good, in terms of football, in the first half. We've been critical of this team over the last 18 months because of the standards City have set, and this team hasn't really reached it, but today in the second half they showed desire, quality.
"It's more than three points. Psychologically, it's a big lift - and a bit of a hammer blow for Arsenal. They still have a nice lead, but to see City go a goal down, and then for them to get three points, huge."
City can cut Arsenal’s gap at the top of the Premier League to just three points when they face Fulham on Wednesday night. Arsenal face Brentford away from home as both sides aim for another 3 points to keep the title race afloat.