The draw sees Phunya Sele Sele climb up to sixth on the log, while Matsatsantsa remain 11th on the table.
Matsatsantsa were hoping to end the year on a winning note when they travelled to the City of Roses having suffered a surprise 3-1 defeat to Baroka FC in their previous league game last weekend.
Morgan Gould, Sipho Mbule and Jeremy Brockie all made their return to the SuperSport starting line-up with Eric Tinkler making three changes to the team that faced Baroka.
On the other hand, Phunya Sele Sele were eager to bounce back to winning ways in the league after succumbing to a 4-1 defeat to Mamelodi Sundowns on Saturday afternoon.
Veselin Jelusic, who missed Celtic's clash against Sundowns as he was attending a coaching course in Europe, named a strong starting line-up with Victor Letsoalo leading the attack and Lucky Baloyi deployed in central midfield.
The match got off to a lively start with both sides looking for the early advantage, and it was Phunya Sele Sele, who threatened first in the opening exchanges following a quick counter attack.
Kabelo Mahlasela dribbled his way into the box and he set-up his Celtic team-mate Ndumiso Mabena, who forced SuperSport goalkeeper Reyaad Pieterse into a great diving save.
The 2017 Telkom Knockout Cup finalists looked dangerous evey time they surged forward and they managed to break the deadlock 15 minutes into the game when Mabena played a brilliant through pass for Letsoalo, who beat Pieterse to make it 1-0 to Celtic.
Matsatsantsa were finding it difficult to unlock the Phunya Sele Sele defence, but they had a rare chance when Thuso Phala was sent through on goal, only for Celtic keeper Patrick Tignyemb to come out and deny him.
Mahlasela, who had a good first half, continued to keep the visitors' defence busy with his pace and dribbling skills in the second half. The diminutive winger combined with Mabena, before forcing Pieterse into a decent save as Celtic looked to double their lead.
With his side struggling to penetrate the Phunya Sele Sele defence, Tinkler pulled out ineffective Reneilwe Letsholonyane and the Matsatsantsa gaffer introduced Siyabonga Nhlapo, who was expected to supply quality crosses into the home side's box.
Brockie should have restored parity for the 2017 Caf Confederation Cup runners-up when he connected with Aubrey Modiba's delightful cross, but the New Zealand international directed his header wide.
The Tshwane giants never lost hope as they continued to probe and another quality cross from Modiba was headed home by second-half substitute Darren Smith to make it 1-1 on his PSL debut, silencing the Siwelele fans inside the venue.
Celtic then pushed for a late winner and Tinkler responded by introducing Thato Mokeke, who joined Dean Furman just in front of the SuperSport defence as the visitors looked to settle for a point.
The hosts were unable to beat Pieterse in the latter stages of the game and ultimately, both teams settled for a share of the spoils.