The visiting side were on top early on and buoyed by their own supporters down in Cape Town, shocked the home side by scoring in the second minute as Nathan Paulse thundered a header into the net following a free kick taken by Cecil Oerson.
Celtic were unlucky not to go into the break two or three goals to the good as they went on to hit the bar on two occasions.
The first one saw Lennox Bacela missing a sitter against his former team as he hit the cross-bar from inside the small box.
And then Paulse's looping headed from a set-piece also went into the woodwork.
Things were balance out slightly when just before the break, Santos' Erwin Isaacs saw his header also striking the bar.
Celtic began the second half on top. But the Cape side slowly started to gain a stranglehold on possession.
However, with 25 minutes to go Bacela should have scored after some fantastic play by right back Kgotso Moleko, but the striker shot well off target.
Gregory Roelf and Isaacs tried in vain to pull a goal back, but they could not force Patrick Tignyemb into making a save.
Phunya Sele Sele had some late chances to add another goal, but Paulse and Mulenga fluffed a couple of chances.