Dean Furman's 80th minute opener was canmcelled out by Banou Diawara's stoppage time equaliser, after the Bafana defence was caught napping.
The hosts also missed two penalties, with Itumeleng Khune saving Jonathan Pitroipa's first half spot-kick before Alain Traore blasted his effort from 12 yards out over the cross bar late on.
Burkina Faso showed early impetus in their backyard as Khune was kept the busier of the two goalkeepers in the first half.
However, it was Bafana who looked to threaten first as Makola blasted a shot narrowly wide of Mohamed Koffi's goal in the opening five minutes.
The Stallions were rather fortuitous just 10 minutes into the match when the Moroccan referee pointed to the penalty spot, despite replays showing that the ball had struck Eric Mathoho outside the box.
Nonetheless, Khune pulled off a stunning diving save to his right to deny Pitroipa, as he not only blocked the penalty shot but managed to deny the Burkinabe any chance of a rebound.
Makola then produced a fine save from Koffi as his low set-pice from just outside the box bounced awkwardly for the Burkinabe shot stopper, who did well to parry the shot away for a corner.
Eight minutes before the break, Prejuce Nakoulma directed a header on target but Khune again thwarted the home side to ensure Bafana go into the break at 0-0.
In the 50th minute, Eleazar Rodgers positioned himself well to get on the end of Makola's cross into the box, but the striker failed to direct his header on target from close range.
Momentum fell in way of the hosts as they piled pressure on the Bafana defence, but Khune was again forced into a spectacular diving save to deny Nakoulma just after the hour mark.
Midway through the half, Oupa Manyisa was brought on in place of Dolly and the substitute almost made his presence felt in the 76th minute but he blasted his effort wayward with only Koffi to beat from five yards out.
Furman finally broke the deadlock in the 80th minute when Makola's corner was uncovincingly cleared and fell for the midfielder, who made no mistake with a right-footed shot through the crowd and into the far corner.
With two minute left of regualtion time, Manyisa needlessly dived into a challenge inside his own area as the referee pointed to the spot for a second time, however, Traore cracked under pressure and ballooned his penalty.
The hosts then poured numbers forward in search of a late equaliser, and they were eventually gifted a goal in the first minute of stoppage time when Diawara was played onside by Abbubakar Mobara and tapped home from point-blank ranger after the defence failed to clear a corner.
Bafana XI: Khune, Mphahlele, Matlaba, Mathoho, Hlatshwayo (c), Kekana (Mahlangu 74'), Makola, Furman, Rodgers, Serero (Mobara 86'), Dolly (Manyisa 65').