The Bafana Bafana attacking duo both scored superb long-range efforts in the first half with the Buccaneers going into the halftime break with a commanding 3-0 lead.
Mofokeng started the exploits in the 16th minute when curled a beautiful effort from outside into the far-corner that thoroughly beat visiting goalkeeper Edward Maova.
Appollis then got into the action on the half hour mark when Deon Hotto teed up the winger to fire in a log-range strike with Maova beaten again.
Pirates were in dominant mood and got a third goal when Ayabulela Maxwele turned a shot from Masindi Nemtajela into his own net in the 36th minute.
The Soweto giants did not take their foot off the gas after the halftime break as Mofokeng completed his brace with neat finish to extend the lead.
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The rampant victory was complete in injury-time when Appollis got his second of the evening when he followed and finished after a shot hit the post.
The result sees Pirates keep the pressure on league leaders Sundowns, with gap still two points with seven games to play.