Dithejane hammered the ball past Sundowns captain and goalkeeper Ronwen Williams and into the net off the post. Shalulile headed the equaliser at the near post off an Aubrey Modiba cross.
Substitute Teboho Mokoena, returning after a hamstring injury, then came close to winning the match for the Pretoria outfit in added time.
If Sundowns avoid defeat at home to seventh-placed Cape Town City on Saturday in the final round, they will become the first Premiership club to complete a league campaign unbeaten.
The stakes are also high for Galaxy as a win at Polokwane City will ensure fourth place and qualification for the CAF Confederation Cup, the African equivalent of the UEFA Europa League.
“We do not have million-dollar players, but we do have million-dollar attitudes,” said Sead Ramovic, the German coach of Galaxy.
He was contrasting his side, which consists largely of little-known South Africans, with Sundowns’ expensively assembled squad that includes five South Americans.
“My team played with so much energy only to let themselves down by not taking more scoring opportunities. Finishing is an aspect of our game that has to improve,” added Ramovic.
Rival coach Rulani Mokwena hailed the fighting spirit of Sundowns as a first league loss loomed since being defeated by Pretoria neighbours SuperSport United in September 2022.
“We struggled at times tonight, but refused to give in. The legs of some players became heavy toward the end, but our magnificent mentalities came to the rescue.”
© Agence France-Presse
Photo: Twitter @Masandawana