The goals were scored by Musa Otieno for Santos and Morgan Shivambu get the equalizer.
Swallows took the game to Santos early on, inspired by live-wire veteran Siyabonga Nomvete.
But it was Birds keeper Greg Etafia who had the first major test – he passed it, thanks to a brave dive at the feet of Orlin Powell after Tony Tsabedze’s cross.
Swallows were nearly on the score-sheet after 24 minutes, but Morgan Shivambu’s glancing header struck the upright after he had been picked out by Nomvethe.
The visitors then found themselves down 1-0 almost immediately afterwards as Santos broke-up field through Tsabedze.
His shot hit a defender, and Musa Otieno was on hand, reacting quickest to place the ball past Etafia.
Swallows levelled the game ten minutes into the second half, thanks to Shivambu, who lashed the ball past Motsoeneng after Bradley Ritson had cleverly placed the ball into his path.
As the game went into the final 20 minutes, Swallows came at Santos with all guns blazing.
After Oscar Machapa and Lefa Tsutsulupa had shots saved, Nomvethe was denied a 77th minute penalty when he looked to have been fouled by Motsoeneng.
Motsoeneng however made a world-class save in the 82nd minute when he dived across to keep out Shivambu’s top corner-bound header.