Divock Origi scored in the 86th minute after the hosts had pegged the Reds back on two separate occasions.
Virgil van Dijk broke the deadlock in the opening quarter of an hour before Christian Atsu levelled. Mohamed Salah then retorted Liverpool's advantage until Solomon Rondon equalised shortly after the half-time break.
Here are five talking points from the match...
Spirited Reds take it down right to the end
So the destination of the Premier League trophy will be determined on the final day of the season.
Liverpool just about found a way to win and the pressure is now on Manchester City to ensure the title race remains in their own hands.