Leopards took one of few chances they created as early as the 12th minute, but Luyolo Mapolisa fired a long-range effort straight at Pirates goalkeeper Moeneeb Josephs.
The Buccaneers struck midway through the first half when Benni McCarthy scored off a deflection, and the hosts held a 1-0 lead at half-time.
They stretched the gap in the second period when Rudolph Bester struck in the 72nd minute.
Benson Mhlongo, playing his first competitive game in two years after recovering from a knee injury, helped set up the goal, and Pirates coach Julio Leal said he was pleased to have the veteran in his squad.
"He's a wonderful player and he's very experienced," Leal said after the game.
"I remember him playing for Pirates three or four years ago.
"He's got a good style and he's one more player who can add value to this squad."
Moses Kwena hit back with a header in injury time to score a consolation goal, but Leopards coach Sunday Chidzambwa hit out at his players for crashing out of the cup competition in the opening round.
"We conceded soft goals and most of our players did not come to the party, especially in the midfield going forward," Chidzambwa said.
"We did not create scoring chances like we normally do, so I don't think we did well today."