The Reds had twice led in the north east through first-half efforts from Virgil van Dijk and Mohamed Salah; however, they were pegged back on each occasion via Christian Atsu and Salomon Rondon.
The visitors then lost Salah to a head injury midway through the second period and the contest appeared to be heading for a draw, until two substitutes combined to secure a vital three points when Divock Origi headed in Xherdan Shaqiri’s free-kick.
The result means Liverpool return to the top of the Premier League table and, regardless of the outcome of Manchester City’s clash with Leicester City on Monday night, the title race will go down to the final day of the season.