Bafana threatened with the first shot on target after Percy Tau cut back inside the box to draw a save from Anthony Silva inside two minutes.
Paraguay though created all the trouble, using their physical strength to bulldoze their way past the thin South Africans.
The South Africans nearly took the lead when Federico Santander beat the offside trap to go one-on-one with Darren Keet but struck the post.
Bafana were struggling to cope with the pressure as Keet was forced to palm his hand out to clear a pass off the feet of Santander following an error by Motjeka Madisha.
Closer to halftime, Tau run at the defence after a long ball but constructed a poor shot which Silva easily saved.
Vincent Pule then came up with a shot from range of his own which crashed against the side-netting on 29 minutes in a good spell of pressure for Bafana.
Paraguay struck and it was none other than Santander tapping home easily after poor defending from Bafana on 33 minutes.
Pule tried to get an immediate reply but after getting goal-side on the side, found his left-footed effort palmed to safety by Silva.
The woodwork saved them then from going further behind after Dominguez twisted and turned Ramahlwe Mphahlele on the right side.
The defensive woes continued from Bafana, as Santander pounced on another error and came close to adding a second but it sailed across goal.
Both nations opted for numerous changes at the start of the second, as the likes of Forune Makaringe, Ronwen Williams, Buhle Mkhwanazi and Dino Ndlovu were introduced.
Bafana were probing for the equaliser in the second half, but they were let down by their decision-making in the final third.
Paraguay, meanwhile, were happy to sit back and soak up the pressure, while looking to catch the South Africans on the break.
Stuart Baxter's men eventually bagged the equaliser with the final kick of the game, as Thulani Serero played in Tau, who side-footed into the corner to salvage a draw.
Bafana: Keet, Madisha, Hlatshwayo, Maela, Mphahlele, Maboe, Mabunda, Mokoena, Pule, Mothiba, Tau.
Subs: Williams, Mkhwanazi, Makaringe, Hlanti, Zwane, Serero, Ndlovu, Lorch.