The goals were scored by Rodney Ramagalela in the first half and Luyolo Mapolisa in the second.
There were no clear chances in the first quarter hour, although Leopards always looked in control of the game.
On 21 minutes an inswinger from Mongezi Bobe was well taken by Bafana Nhlapo inside the six-yard box.
Five minutes later Mazwi Mncube tried a shot but it went over the bar.
On the half hour mark, Thabo Mongalo snuck inside a defender, but his attempt was well taken by Nhlapo, before a shot from Raymond Monama went over the bar.
At this stage Leopards were attacking with purpose, with Mapolisa and Nkosiyabo Xakane combining well.
Mongalo put a header over the bar, with no keeper to beat, but Ramagalela made it 1-0 soon after, clinically beating Nhlapo at the near post.
Leopards kept up the tempo going into the break, but the frantic first half ended 1-0.
Leopards continued where they left off in the second half, although in the 56th minute a poor clearance from Ernort Dzaga almost gave Blackburn the equaliser.
In the best chance of the second half, Ramagalela, with only the keeper to beat, managed to hit wide.
With Blackburn in the hunt for an equaliser, finally Leopards got their second, through Mapolisa.
Mapolisa then missed the chance to make it 3-0, when he blasted a shot over the bar after a defence splitting pass from Itumeleng Duiker.
There was a good turnout at Giyani Stadium, with 12 000 supporters rooting for the home side.
Leopards languish in the relegation zone of the Premiership, but this Nedbank Cup result will be a boost to Vladislav Heric's men, as they look to repeat their final appearance of last season.