The result means that Pep Guardiola’s side remain one point ahead of the Merseyside club with seven league matches remaining.
Both teams will face each other again next Saturday in the FA Cup semifinal.
Ederson almost scored a comical own goal just after the half an hour mark following a back-pass but managed to clear the ball away before it crossed the line.
City started the gain the upperhand and went back ahead after 37 minutes when Jesus managed to stay onside and finish off Joao Cancelo’s cross at the back post.
Just before the break, Jota was put through on goal but Aymeric Laporte produced a fine last-ditch challenge to prevent the equaliser.
Liverpool grabbed an equaliser 48 seconds into the second half when Mohamed Salah set up Mane to smash the ball into the top corner.
Sterling thought his strike had regained the lead for the hosts after the hour mark but the goal was ruled out for offside by VAR.
Substitute Riyad Mahrez had a golden opportunity in the final seconds but lofted his close-range effort over the bar.