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 three-and-a-half weeks ago, Lions head coach Ian McGeechan has already seen Stephen Ferris, Leigh Halfpenny, Ryan Jones and Euan Murray ruled out of the tour through injury, while James Hook was unavailable for selection for the first Test after taking a heavy knock during Tuesday's win over the Southern Kings.
Those injury setbacks 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.
"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 me, 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.