Needing a win and a City defeat to capture the league, Liverpool fell behind to a Martin Skrtel own goal.
But the match turned around when Daniel Agger and Daniel Sturridge converted Steven Gerrard free-kicks.
Newcastle striker Shola Ameobi saw red for dissent and team-mate Paul Dummett was sent off for fouling Luis Suarez.
Liverpool had been in control of the title race with three games remaining before a 2-0 defeat by Chelsea and a 3-3 draw at Crystal Palace handed the initiative to City.
A 2-0 victory over West Ham for Manuel Pellegrini's team on Sunday ensured Liverpool's result was academic.