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The Buccaneers started strongly and set the tone for encounter with two attempts on goal within the five minutes through Ghampani Lungu and Moremi.
The hosts kept up the pressure and eventually took the lead in the 15th minute when Thapelo Mokobodi found the back of the net after being set up by Moremi.
Milford were being outclassed and Pierates were still doing all the attacking as Thalente Mbatha and Evidence Makgopa also wet close to doubling their tally on the scoreboard.
Moremi made it 2-0 just after the half hour mark when the winger rounded the keeper before providing the finish after the through ball from Mbatha.
Mpho Padime came off the bench for the injured Lungu in the first half, and the youngster made an immediate impact when he set up Moremi to complete his brace.
Milford showed a bit more attacking verve after the interval but were ultimately not good enough against Pirates, who march into the next round of a cup that they won last season.