It wasn't just about the 1962 FA Cup Final - where we beat the Clarets 3-1 at Wembley - but a rivalry that stretched over four seasons and included three-successive meetings in the FA Cup.
To get an understanding of where the teams stood in that era, a glance at the First Division table from 1959-60 through to 1963 sums it all up.
Burnley won the title in 1960, we did the double in 1961, Burnley were second and we were third in 1962 while we were second and Burnley third in 1963.
At the same time, we beat Burnley in the semi-final of the FA Cup in 1961, beat them in the final in 1962 but then lost in the third round in 1963.
It's no wonder 50 years on that Cliff admitted the draw for the third round 'brought back a few memories'.
"We were the teams at that time, we put bottoms on seats," said Cliff. "They were special times."
Pictured, above: FA Cup success in 1962.
Watch Cliff's interview in full at the top of the page...