A tight opening characterised by solid defence on both sides saw a Roberto Firmino shot from distance as the only notable effort inside the first 20 minutes, before Carlitos could only slice over after good work on the edge of the box for the hosts.
Firmino shot straight at the goalkeeper as Jurgen Klopp's side attempted to exert some control on the game, and Divock Origi came close to adding to his hat-trick against Southampton last week when his shot flew narrowly wide.
The game opened up as the first half wore on, and Reto Ziegler's volley from distance came close for Sion before Adam Lallana should have done better from 18 yards after he did well to make space for himself on the edge of the penalty area.
Liverpool ended the first half on the front foot and they began the second period in the same way, but James Milner inadvertently prevented an unmarked Firmino from meeting Origi's cross at the far post as they continued to struggle for a killer final touch.
Sion knew that a draw would send them into the last 32 and their defence stood resolute as they allowed the Reds to dictate the tempo of the second 45.
The best opportunity of the latter stages of the match fell to Liverpool, but they were denied by Andris Vanins as the goalkeeper did well to deny Origi after substitute Philippe Coutinho had flicked Emre Can's ball through to the striker.
The match fizzled out with barely another sniff of goal as Sion settled for the single point which saw them progress to the knockout stages, while Liverpool completed an unbeaten group-stage campaign to top the group.