Best known for his work with two-time Open champion Padraig Harrington, the 82-year-old Scot was widely renowned as one of the greatest coaches in the sport.
His impact on many golfers - professionals and amateurs alike - was clear by the turnout, which included Paul McGinley, Scott Henderson and Harrington. His son Sam, who captained Europe to Ryder Cup success in 2002, poured out a dram of whisky in memory of his father at the Greenock Crematorium service.
"Of course I drank most of it on the way here," he said, laughing back the tears, before making a toast: 'To dad'."
Torrance's death from lung cancer cast a shadow over the 143rd Open Championship after Sam announced that he had passed away on July 18.
Sam told a number of stories about his father - and coach - before saying: "He was a very special man and I will miss him so much. The response since he passed away has been exceptional, I can't thank you enough."