Cotton then managed the 1997 tour that also ended in a series triumph over the Springboks.
This year, however, he believes the Lions will face an even tougher challenge with the hosts gunning for revenge.
"The Lions this year do have a real chance but I think South Africa will be better prepared," said Cotton.
"There are lots of similarities with 1997. The opposition are world champions and the Lions are underdogs although not quite as big underdogs as they were in '97.
"Back then the fans hadn't seen the Lions for 17 years and they had almost forgotten about what the Lions are. This time it's fresh. The South African players have all been talking about facing the Lions as they realise it's a once in a lifetime chance for them."
Since arriving in South Africa, Lions head coach Ian McGeechan has already seen Andy Powell and Stephen Ferris ruled out of the first tour match against the Royal XV, while Keith Earls was then unavailable for selection against the Golden Lions this Wednesday.
Those minor injuries are in addition to the changes that were forced upon McGeechan and his fellow coaches prior to departure for South Africa when Munster scrum-half Tomas O'Leary, Cardiff Blues centre Tom Shanklin, and Munster duo Alan Quinlan and Jerry Flannery were ruled out of contention for the entirety of the tour.
Cotton admits that the early injury situation has been worrying for all involved but, now that the Lions have begun their 10-match tour, he says McGeechan will be desperate to avoid injuries to his key players such as though which blighted the 2005 tour to New Zealand when the likes of Brian O'Driscoll, Richard and Lawrence Dallaglio suffered injury setbacks.
"The Lions usually have six or seven players who get injured before the Tests and we are already seeing that," said Cotton.
"But there are some certain players who are irreplaceable to the Lions and I just hope we get to the first Test with them all fit and well and then we have a chance."
As with every Lions tour, the task facing the Lions management team is to create a winning team from the best players from the Home Nations and Cotton is hoping they can conjure something special like their 1997 predecessors.
"Looking back at '97, you knew you had a great set of players but you never knew if they are going to bond," he explained.
"For m, the moment I realised they were a very special set of players was the morning after the first Test. After a tough match it would have been so easy for the players to go out on the beers in Cape Town.
"But the next morning all the Test players got up and went training with the midweek players who were preparing for a game against the Free State.
"That was the bond those players had and that's what made '97 and '74 so special. The players would do anything for each other."
Fran Cotton was speaking at an HSBC Lions Legends event in aid of the Lions Charitable Trust .