A fraught affair in the 230th meeting between the Merseyside rivals saw the Reds lead at the break courtesy of a calmly-taken James Milner penalty.
Jürgen Klopp's side enjoyed the better of the encounter but Gylfi Sigurdsson's goal on the counter-attack levelled the score midway through the second half.
The night belonged to Van Dijk, though. The towering defender was first to a Kop-end corner and nodded home with six minutes remaining to secure a 2-1 success.
See the story of the game in photographs below...