Thorburn reached the final of the 1978 Masters with wins over Doug Mountjoy and Spencer, losing 5–7 to Higgins in the final. He was knocked out of the 1978 World Snooker Championship by Charlton, 12–13 in the quarter-finals. In the 1978–79 snooker season he defeated Tony Meo 17–15 in the final to win the 1978 Canadian Open after having trailed 6–10 at the end of the first day of the final, but lost his opening matches in both the Masters (4–5 to Perrie Mans) and the World Championship (10–13 to John Virgo). He retained his Canadian Open title in 1979, taking a 10–3 lead over Terry Griffiths before winning the match in the deciding frame, at 17–16.