Ernst Middendorp made three changes from their defeat to Cape Town City as goalkeeper Daniel Akpeyi was given his debut, while George Maluleka and Leonardo Castro also got the nod to start.
On the opposite side, Milutin Sredojevic made only one change from their goalless draw against Esperance in the CAF Champions League last Saturday as Happy Jele started ahead of Marshall Munetsi.
The match got off to a pacey start and Ben Motshwari should have given Bucs the lead in the 11th minute after going clear on goal, but Amakhosi defender Teenage Hadebe made a brilliant sliding tackle to make a crucial block.
The pace was slowed down towards the half-hour but Justin Shonga had a glorious opportunity to break the deadlock, but he was unable to get on the end of Vincent Pule's inviting cross from the left flank.
There were no clear chances in the closing stages of the half as both Wayne Sandilands and Akpeyi had a relatively easy opening 45 minutes.
Middendorp made his first change at the beginning of the second stanza as youngster Happy Mashiane was withdrawn for Philani Zulu.
Amakhosi finally found the breakthrough three minutes later from a composed penalty by Daniel Cardoso after Asavela Mbekile brought down Billiat inside the box, 1-0.
Sredojevic made his first substitution on the hour-mark as striker Augustine Mulenga came on for Musa Nyatama while Chiefs responded by introducing Willard Katsande for Castro five minutes later.
Lorch eventually restored parity ten minutes before time as he latched onto Ben Motshwari's pass before rounding Akpeyi and finishing from a tight angle.
It was anybody’s game in the closing stages but neither side could find the winner as the two Soweto heavyweights shared the spoils on the day.
Chiefs: Akpeyi, Moleko, Ntiya-Ntiya, Hadebe, Cardoso, Maluleka, Ekstein, Parker, Mashiane, Billiat, Castro.
Subs: Bvuma, Katsande, Mphahlele, Zulu, Ngezana, Paez, Ntshangase.
Pirates: Sandilands, Mbekile, Maela, Ndengane, Jele, Motshwari, Lorch, Mlambo, Nyatama, Shonga, Pule.
Subs: Mabokgwane, Munetsi, Mako, Mntambo, Makola, Mahachi, Mulenga.