Sundowns looked to be heading to three points and top spot on the table as they led 2-1 in second-half injury-time, only for Baroka to win and convert a late penalty to rescue a vital point.
The result left Down two points adrift of leaders Bidvest Wits, who suffered a shock loss to Free State Stars in a simultaneous kick-off.
The Brazilians made the breakthrough after just seven minutes as Thapelo Morena found space out wide before putting the ball into the box, where Khama Billiat ran in unmarked between two defenders for a simple tap-in past a stranded Oscarine Masuluke.
The Zimbabwe international was proving the liveliest outlet for Downs in the first-half and did well to hold up play in the box before laying off for Themba Zwane, but a rush of blood to the head saw the attacker blaze his shot miles over the bar.
Baroka finally got their first shot on target after 28 minutes as Maboke Matlakala rose well in the area to win his header, but it lacked any significant power and Denis Onyango eventually made a comfortable save.
The half ended in a flurry with two injury-time goals, Mzwanele Mahashe scoring a bizarre own-goal with a back-pass that bounced over his goalkeeper's attempted clearance, before making amends at the other end with a powerful header to pull one back.
Baroka almost found a way back three minutes after the break as a superb delivery into the area from a free-kick left Sundowns scrambling, with Onyango eventually colliding heavily with Tiyani Mabunda, although the Brazilians eventually managed to clear their lines.
Bakgaga then had a golden chance to make it 2-2 with around 20 minutes remaining as the ball was played over the top before falling kindly for Victor Letsoalo right in front of goal, but the forward got his attempt all wrong and ended up swiping at fresh air to allow the Downs defence to clear.
Billiat threatened to grab his second of the night after doing well to control a cross in the area before faking a shot and turning his man to open sight of goal, although his shot was rushed and he eventually skewed wide of the mark.
Sundowns threatened to wrap the game up with six minutes remaining as Percy Tau broke down the wing in a swift counter attack, although Anthony Laffor went to early, forcing a decent move to come to nought after the flag was raised for off-side.
And, Pitso Mosimane's men were made to pay for that miss as Baroka struck the vital equaliser with 93 minutes gone, Morena fouled for a hand-ball in the area, with Richard Matloga stepping up to fire home from the penalty spot.