The Cape Town side could have closed the gap at the top of the table to just two points behind city rivals Ajax and Supersport United, but instead are four points adrift with four games to play.
It was a game of firsts as Tawonga Chimodzi scored his first goal for Santos just before halftime, before Mokete Tsotetsi replied with his first for Chiefs 15 minutes into the second half.
The home side made the brighter start, but it was their young goalkeeper Itumeleng Khune who prevented them from going behind on 23 minutes. A cross from Romano Scott was met brilliantly by Chimodzi, whose point-blank shot was brilliantly saved by the Bafana Bafana stopper.
It was a rare chance in a first half that saw both defenses on top, but Amakhosi did have efforts through Mabhuti Khenyeza and David Mathebula, both of which went wide.
The breakthrough finally came just a minute before halftime when the lively Chimodzi found space in the box after great work by Eleazar Rodgers and fired home from six yards past a despairing Khune.
Fabian McCarthy forced a good save from Wayne Roberts in the visitors’ goal with a header from close-range, while Khenyeza did likewise with a flick from barely three yards out.
But the equaliser did come on 60 minutes when Mathebula’s excellent set-piece from the right was powerfully met with his head by Tsotetsi, who left Roberts with no chance.
McCarthy almost scored a winner when his header at the back post flashed across goal and shaved the opposite up-right, while Kaizer Motaung Jnr should have made a better connection with his header which might have sealed the points for the home side.
Roberts then made a fine save from Arthur Zwane, while Motaung Jnr shot wide as Santos hung on desperately in the final few minutes.
Chiefs’ players then believed they should have won a penalty as the ball struck the arm of Musa Otieno, but referee Jonas Nhlapo waved away their protests.