Sampson, who made his TV debut against 20-year-old Barry, won 3-1.
This result comes after the 40-year-old beat compatriot Devon Petersen on his way to Alexandra Palace.
The South African will now face off against Belgium's Huybrechts.
Sampson stuns Barry on TV debut at World Darts Championship
South Africa's Grant Sampson has sensationally beat Keane Barry, of Ireland, to set up a clash with Kim Huybrechts at the World Darts Championship on Friday.