Captain Lucky Lekgwathi converted the winning spot kick as the Buccaneers won the shootout 4-3 at Mbombela Stadium.
Victory took the former African champions into the semi-finals draw Monday with Wits University, Platinum Stars and Kaizer Chiefs.
SuperSport led in regular and extra time through an own goal from left-back Thabo Matlaba and Botswana midfielder Mogogi Gabonamong.
But close-season signing Lennox Bacela, an early substitute for injured Zambia striker Collins Mbesuma, levelled twice.
The thrilling tussle was a welcome relief to the 15 000 crowd and a pan-African TV audience after three one-sided quarter-finals
Wits, Platinum and Chiefs each triumphed 3-0 against Bloemfontein Celtic, Free State Stars and Pretoria University respectively in one-sided quarter-finals.
The history of Pirates-SuperSport clashes pointed to a close encounter and so it proved in perfect cool, dry late winter conditions.
"We dug deep and gave everything -- I have a team of warriors who deserved the victory," Pirates coach Roger de Sa said.
SuperSport boss Cavin Johnson said: "Penalties are always a lottery and it was disappointing to lose after leading twice."
Matlaba back-headed a long Thabo September throw over goalkeeper Senzo Meyiwa on 31 minutes with the ball entering the net via the crossbar and a post.
The equaliser on the hour mark came gift wrapped as a careless clearance by Sibusiso Khumalo fell to Bacela, who fired past Ronwen Williams.
When Meyiwa failed to hold a high cross under pressure from Senegalese giant Mame Niang early in extra time, Gabonamong stabbed the ball over the line.
But Bacela rescued Pirates six minutes from time, giving Williams no chance with a close-range shot off a low cross.
An unhappy afternoon for Khumalo ended three minutes from time with a red card after a second caution.
Scores:Orlando Pirates: (0) 1 ET 2 (Bacela 61’, 113)
SuperSport United: (1) 1 ET 2 (Matlaba OG 31’, Gabonamong 93’
Penalty shoot-out: Williams (missed), Jali (missed), Niang (goal), Erasmus (goal), Maluleke (goal), Mahamutsa (goal), September (missed), Bacela (goal), Fransman (goal), Lekgwathi (goal).