Pirates won a stoppage-ridden quarter-final second leg 1-0 in Soweto thanks to a headed goal from forward Peprah, with TV replays shown belatedly suggesting he was offside.
The only goal came just after Democratic Republic of Congo-born Simba forward Crispin Mugalu, who had been cautioned earlier, was shown a red card for a studs-up tackle.
Peprah tied an ill-tempered two-leg showdown at 1-1 on aggregate after Simba won the first encounter through a disputed Shomari Kapombe penalty in Dar es Salaam last Sunday.
Unlike Europe, where UEFA ties go to extra time first, Africa heads straight to penalties and Pirates won the shootout 4-3 with goalkeeper Ofori converting the kick that took the Buccaneers through.
Pirates will know who they face next only at midnight South African time as the Libyan derby between Al Ahly Tripoli and Al Ittihad begins at 2000 GMT in Benghazi.
The late kick-off is due to the Muslim holy month of Ramadan, with most players observing a dawn-to-dusk fast, then eating and drinking before preparing for matches.
Ahly or Ittihad, whose first leg ended goalless, will have home advantage over Pirates on May 8 with the return match on May 15. No date or venue has been announced for the final.
– Controversial decisions –
The penalty shootout drama compensated the crowd at Orlando Stadium after a match constantly punctuated by long delays for injuries, mostly to Simba players.
Apart from the goal, there were several other controversial decisions with Pirates twice having genuine penalty appeals rejected by a referee from the Seychelles who struggled to keep control.
Namibian Deon Hotto, Malawian Frank Mhango, Tshegofatso Mabasa and Ofori converted shootout kicks for Pirates and Kapombe, captain Mohamed Hussein and Rwandan Meddie Kagere for Simba.
The other semi-final in the African equivalent of the UEFA Europa League will pit TP Mazembe of DR Congo against Al Masry of Egypt or 2020 Confederation Cup winners Renaissance Berkane of Morocco.
Masry, whose best showing was reaching the 2018 semi-finals, lead 2-1 on aggregate ahead of the second leg in northeastern Morocco on Sunday (2200 GMT).
After forcing a goalless draw away to Pyramids of Egypt last weekend, Mazembe were favoured to win the return match at home and they overcame missing a penalty to triumph 2-0 on the day and on aggregate.
Christian Koffi atoned for his spot-kick miss by breaking the deadlock on 33 minutes in the southern city of Lubumbashi and Jephte Bola added a second goal just before half-time.
Mazembe are chasing a record-equalling third Confederation Cup title after lifting the trophy in 2016 and 2017.
Tunisian outfit CS Sfaxien, who failed to get beyond the group stage this season, won the competition in 2007, 2008 and 2013, when they edged Mazembe in the final.