Bay went ahead through Paulus Shiphanga and Siyabulela Songwiqi, before Chiefs came back before half-time through Jose Torrealba and Thabang Rooi.
Bay took the lead again through Jermaine Christian on 55 minutes, before Chiefs were awarded a penalty just before full-time, converted by Gert Schalkwyk.
Although the heat in Rustenburg was almost unbearable, things looked good for Chiefs early on when Torrealba fired over the bar with less than a minute's play on the clock.
However, only a minute later Bay United took a shock lead when young Namibian Shipanga netted from a tight angle after a glaring mistake from Chiefs left back Onismor Bhasera.
Bhasera totally misjudged a seemingly harmless long-ball, allowing the ball to drop behind him and into the path of Shipanga, who showed good composure to take a single touch before finishing from a tight angle.
The goal left the home side stunned, and it was soon to get worse as Umlilo doubled their lead after just seven minutes when Vincent Khumalo beat the off-side trap and unselfishly crossed for Songwiqi to score from close range.
Amazingly, the Port Elizabeth side came within inches of adding a third when Gareth Ncaca thudded a free kick into the crossbar.
Having survived what could have been a killer blow, Amakhosi slowly started to play their way back into the game, putting increasing pressure on the Bay United defence.
In the 25th minute a quick break down the right saw Zito Ogbanna sliding in a perfect cross for Torrealba, who made no mistake in sliding home the ball and in the process cutting the deficit in half.
Khumalo had a great chance to restore the visitors two goal lead when he again beat the off-side trap, but poor control let him down and the opportunity went to waste.
If was Chiefs though who had slowly been taking hold of the game and it came as no surprise when they equalised just before the half time break, via an unlikely goalscorer in defender Rooi.
Rooi capitalised on Bay United’s inability to clear their box after a Chiefs free-kick by stabbing the ball into the back of the net with his left foot from eight yards out.
The balance of play for the second portion of the first half suggested that it was Amakhosi who were in the ascendancy, however, following a relatively incident-free start to the second half, it was Bay United who scored the next goal, in the 55th minute.
Christian was the goal-scorer, belting a thunderbolt of a free kick into the top corner of the net.
Chiefs were soon back on the offensive, but the PE side managed to do just enough to keep them at bay, although defender Patrick Mayo did seem rather fortunate not to have being penalised for a handball.
With Chiefs pushing forward for an equaliser, and having brought on Mandla Masango for defender Jonathan Quartey, gaps were always going to be opened up at the back.
In the 75th minute Jimmy Zakazaka should have profited from one such occasion when Rooi allowed him to run clean through on goal, but his parting shot was too close to Khune, who managed to block the shot.
Zakazaka was guilty of missing another great chance to seal the game just a minute later when he ballooned a shot over the bar with only Khune to beat.
The Soweto side were handed a life-line in the 88th minute when former Chiefs player Mayo was deemed to have fouled Mandla Masango inside the box.
Schalkwyk made no mistake from the spot to level the game at 3-3, which was the final score, despite a late rally by Chiefs which saw Siphiwe Tshabalala come agonisingly close with a well-struck volley.