The same fixture on 2 January 1971 ended in tragedy as 66 Rangers supporters were killed after being crushed in a stairwell when leaving Ibrox. Smith, now the Rangers manager, was at that game as a supporter and considers himself lucky to have escaped unharmed.
"I hadn't been picked for the Dundee United game that weekend and so I was home in Glasgow and I went to the game," Smith said. "Coming on buses from Carmyle, it was the Rangers end where we all congregated, and my brother and I were both caught on the stairs.
"It wasn't unusual back then for the crowds to feel the squeeze on that staircase – there was always a bit of a bottle-neck at the bottom of it, and the crowds often had to stop. So I didn't think that much of it at the time.
"We managed to scramble out over a fence, which I thought was down the way, but when I've subsequently seen photographs of where we got out, it wasn't down. So we must have climbed over the top of some other people in order to get out on to Edmiston Drive."
Smith explained that the full scale of the incident – a further 145 supporters were injured – did not become clear until he returned home. "We then got on to our bus and went away home," the 62-year-old said. "Communication back then wasn't what it is today. There was nobody on the bus who was really talking about it much at all. It was only when we got back to Carmyle, where everybody was congregating and waiting to see if everybody was OK, that we realised there had been a disaster.
"You just feel fortunate, when you are that close to something like that, that you get out without coming to any harm. You consider yourself very fortunate."
A memorial service will be held at Ibrox on Monday morning to mark the 40th anniversary. A minute's silence will precede the derby a day earlier, with members of the Rangers and Celtic squads from 1971 taking to the field. Players will also wear black armbands during the Scottish Premier League match.
The occasion will register with Smith more than most. "My brother and I were about a third of the way down the stairs," he said. "I think the majority of the people who died were further down the stairs, around the bottom third. So, like I say, when we found out later what happened, we realised how fortunate we had been.
"I can just remember people there telling us that there had been a terrible disaster at Ibrox. On our bus we all went to the same sort of area of the ground and we had no one that got injured. We left Ibrox that day having no idea that anything like that had occurred. It wasn't until we got home that we heard about it.
"It was a disastrous day for everyone. We were the lucky ones, the fortunate ones."
guardian.co.uk © Guardian News and Media Limited 2010