AmaKhosi headed into the clash knowing a victory would seal third spot and a place in next season's CAF Confederation Cup.
The game got off to a slow start as both sides looked to find their rhythm in the opening 10 minutes of the encunter.
Ajax went agonisingly close to breaking the deadlock on 22 minutes when Roscoe Pietersen rattled the woodwork following a corner from Fagrie Lakay.
Brilliant Khuzwayo, who replaced the injured Itumeleng Khune, was called upon after 35 minutes as he produced a fine save to deny Yannick Zakri the opening goal.
Chiefs went close to taking the lead just before the break, but Jody February produced a superb save to deny Benard Parker from close range.
Chiefs broke the deadlock six minutes into the second half when Parker rose well to head home from a corner.
Ajax pushed for an equaliser and they went close in the 62nd minute through Tashreeq Morris, who was denied by a fine save from Khuzwayo.
The Urban Warriors were level moments as captain Mosa Lebusa rose above his marker to send a towering header past Khuzwayo at the far post.
Khuzwayo proved to be the busier of the two goalkeepers as he produced another fine save deny Pietersen with 15 minuets remaining.
However, Chiefs secured the win with four minutes remaining thanks to a close-range finish from Joseph Molangoane.