The Canadian reclaimed his PDC Tour Card at the Q-School a month ago, after having one in 2012 and 2013. At his return Smith won four matches to set up a clash with Wright.
The former Lakeside finalist started well and took a 5-1 lead, before his Scottish opponent won the next four legs. However Smith had the throw in the decider and he used this advantage with a 15-dart leg.
'The Silencer' faces Brendan Dolan in the semi-finals, who defeated Dutchman Maik Kuivenhoven in his very first PDC Quarter-Final. Dolan also knocked out number one seed Michael van Gerwen earlier in the tournament.
Gary Anderson and Adrian Lewis will meet in the second semi-final. Anderson saw off Joe Cullen, while Lewis booked a victory over Steve Beaton to reach the last four.
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Brendan Dolan 6 | 5 Ross Smith
Maik Kuivenhoven 6 | 3 Steve Brown
Peter Wright 6 | 3 Conan Whitehead
Jeff Smith 6 | 5 Nathan Aspinall
Adrian Lewis 6 | 1 Darren Webster
Steve Beaton 6 | 1 Mickey Mansell
Gary Anderson 6 | 2 Rob Cross
Joe Cullen 6 | 1 Nick Kenny
Brendan Dolan 6 | 3 Maik Kuivenhoven
Jeff Smith 6 | 5 Peter Wright
Adrian Lewis 6 | 3 Steve Beaton
Gary Anderson 6 | 2 Joe Cullen
Brendan Dolan - | - Jeff Smith
Adrian Lewis - | - Gary Anderson