Darwin Nunez spurned a golden chance to put Liverpool 2-0 up inside the first half after somehow managing to hit the post with the goal at his mercy.
Mo Salah put the visitors ahead at Ajax in the 42nd minute, but just two minutes later the Uruguayan was given an opportunity to double the ascendancy just before half-time, but he was unable to convert Roberto Firmino's pass.
However he did quickly atone for his error after just four minutes in the second period, with a strong header from the centre of the box off an Andy Robertson corner.