Birds' caretaker coach Fani Madida made seven changes from their 3-2 loss to Mpumalanga Black Aces on October 18, and the gamble paid off with Swallows getting a valuable point.
However, it was Chiefs who had a better start with Mandla Masango combining with Erick Mathoho, but the latter's shot over from outside the box in the seventh minute.
Both teams were having a slow start and the next chance, though not clear-cut, fell to Reneilwe Letsholonyane in the 23rd minute, but his attempt was way off target.
At this stage there had been no real chances from either side, but a goal by Swallows in the 28th minute changed the complexion of the match.
Lucky Baloyi, on loan from Chiefs to Swallows, beat Brilliant Khuzwayo with a shot from outside the box to silence the fans of his parent club.
Swallows could have got another goal barely three minutes later, but Vuyisile Wana, who was picked up by a brilliant pass by Baloyi wide on the left, couldn't take advantage as his left-footed attempt went accross of goal.
Chiefs had a great chance to level matters a minute later when Lebese played the ball into Letsholonyane's path, but the midfielder's chip over Greg Etafia failed to hit the target.
Two minutes later, Tsepo Masilela surged forward down the left, picked up Kingston Nkhatha in the box and the Zimbabwean international laid it on for Masango, whose shot was tipped over by Etafia for a corner which failed to produce a goal.
Chiefs had a penalty appeal turned down in the 41st minute when the ball came off Siphiwe Tshabalala and appeared to hit Tsietsi Mahoa's left hand, but referee Zolile Mthetho didn't see it that way and allowed play to continue.
For the first time this season, Chiefs went into the break on the losing side.
After the interval, Chiefs went on the offensive in search of an equaliser while Swallows sat back in an attempt to defend their lead.
Chiefs piled on the pressure and got their reward in the 67th minute after Lebese, Masango and Letsholonyane combined to great effect, with 'Yeye' on the end of Masango's header forward in the box to make it 1-1.
It was all Chiefs at this stage and Shabba thought he had won a penalty in the 70th minute after it appeared he had been hacked down by Larry Cohen, but instead he was cautioned for a dive.
In the 75th minute Masango started a great move, passed the ball on to Lebese who laid it on for Tshabalala, whose attempt from close range was wide.
That's how it ended with both teams playing to a draw for the first time this season.