The Glamour Boys, eager to bounce back, struck first in the 36th minute through Wandile Duba, who pounced on a rebound after Gaston Sirino's powerful shot was parried by TS Galaxy goalkeeper Ira Tape.
Duba had earlier been involved in a promising sequence, winning a free-kick which Nkosingiphile Ngcobo curled towards goal, only for Tape to deny it.
TS Galaxy, however, remained resilient. Despite an earlier blunder from Letsoenyo Kganyana that led to Chiefs' opener, the Rockets fought back.
In the second half, Mlungisi Mbunjana capitalised on a moment of chaos - Bruce Bvuma had saved Edmilson Dove's deflected clearance, but Mbunjana was quickest to react, levelling the score in the 81st minute.
The match was peppered with chances. Sirino missed a gilt-edged opportunity after Mbunjana carelessly gave away possession, while Glody Lilepo failed to hit the target from a Duba cross in the first half.
Substitute Siphesihle Maduna added fresh legs for TS Galaxy after Mpho Mvelase made way in the 55th minute, as Adnan Beganovic's side pushed for a winner.
In the dying moments, Puso Dithejane missed a golden chance to snatch all three points for the visitors, slicing wide when it looked easier to score.
TS Galaxy's dramatic transformation from relegation contenders to top-three hopefuls is gaining momentum, and head coach Adnan Beganovic believes his side is ready to challenge for a spot in African competitions next season.
Kaizer Chiefs coach Nasreddine Nabi believes that his team's recent struggles are not as a result of bad luck but rather an opportunity for the squad to take charge of their destiny and turn things around.
Kaizer Chiefs coach Nasreddine Nabi says poor finishing cost his team once again as they drew 1-1 with TS Galaxy in the Betway Premiership on Sunday.
Kaizer Chiefs defender Reeve Frosler is hopeful of securing a new contract with the Soweto giants.
