Smith won comfortably, recording three 180s and winning nine legs from a possible nine to advance to the next round.
Rafferty had just edged Dutch opponent Jermaine Wattimena on the opening day of the tournament to set up a tie against last year's runner-up.
'Bully Boy' reached the final of the World Championships last year but fell at the last hurdle against Peter Wright, who won his second world title.
Wright was also victorious in his opening match this time around, beating Michael Mansell 3-0.
