His former club have since made plenty more moments when they have simply lost. Among the most painful have come when sharing a pitch with Celtic given 19 years have passed since Shaw scored to inflict a 1-0 defeat on the Parkhead side. It was a towering result back then but has only grown in significance as it is still the last time that Thistle won at home against Celtic, a period of sparse reward stretching back to that day on January 8, 1994.
It was a date marked by celebration but it also carried major financial ramifications. Shaw's famous goal inflated the transfer fee Dundee would be forced to pay for his signature just three days later, when the Tayside club agreed deals for both the forward and his strike partner Gerry Britton, with the final sum enough to fund for the construction of the Jackie Husband Stand which will house both Thistle and Celtic supporters on Sunday.
That will evoke memories of his historic strike for Shaw, although he would gladly share the limelight with one of the Firhill club's current players. "I would love to give someone else this record and what a boost it would for Thistle if they could beat Celtic on Sunday," said Shaw, who is still playing football at the age of 44 as player-manager of Strathclyde Evangelical Churches League side, Kilsyth United. "I've had my time so hopefully someone can come in and take the mantle from me.
"I'll never forget that game. Celtic had had umpteen chances when we got a free-kick - Chic Charnley threw the ball in and I managed to sneak in at the back post and volley the ball into the net. It was great for the supporters and hopefully they can get another result like that this weekend."
Shaw did not miss a step as he walked back through his past and he remains tickled by the circumstances which followed as he made his way to Dundee the very next week. "Jim Duffy reckoned it pushed the price up; he called me up after that Celtic game and said 'Thanks a lot you've just cost me an extra £125,000'," he said. "It was the following Tuesday when Gerry and me both left for £250,000 - and I think that paid for the new stand at Firhill."
Since their stunning 4-1 League Cup final victory over Celtic in 1971, Thistle have only beaten their Glasgow neighbours five times and Shaw was also happens to have been the goal hero the last time the Firhill team won at Parkhead, in 1992. It was an occasion which nearly ended in his arrest.
"I could have had a hat trick," said Shaw. "I remember Paul Kinnaird dropping the shoulder and putting the ball over and I made a run to the front post and headed it in. At the start of the second half Andy Payton scored, then I had another chance when Albert Craig played me in but I hit the side net. Then we got a corner and the ball just bounced in front of me and I managed to slide in and score. I've actually got a photo of that goal at home and you can see John Collins stretching to block the shot but it goes over his head.
"I jumped the barriers to celebrate with the Partick supporters and after the game we had a knock on the dressing-room door and it was the police. They said to John Lambie that I could have caused a riot and they wanted to talk to me. But John said: 'When was the last time Partick Thistle came to Parkhead and won? Leave the lad alone, he's just scored two goals'. Thankfully they left."
Shaw's reflections are barely disturbed by the ripples they once created, but he tends to spend most of his time these days looking ahead in his role as a Thistle scout. His report contributed to the side registering a win against Inverness Caledonian Thistle last weekend and he has already handed over his dossier to manager Alan Archibald having watched Celtic draw against Hibernian last Saturday.
"What I have seen of Thistle they have done very well," he said. "I was at the St Mirren game earlier in the season and they were outstanding, Archie's got them playing really good stuff. They are organised and very tight and, while they could do with scoring more goals, that will come.
"It's a learning process having come up from the first division and they are adapting to the pace. They are probably finding they have more time on the ball I'm sure Archie will keep them up. He has done a fantastic job so far. I was at Easter Road and Hibs worked really hard and deserved a point.
"I think their goal was offside right enough and Celtic had plenty of chances. But that's what you are hoping for when you play against either of the Old Firm. They need to have an off day and you need to have a good day."