The first real effort on goal came after six minutes when Phikolomzi Kefile rifled in a blistering volley from 25-yards out, which Patrick Tignyemb did well to palm to safety.
Having settled into a positive tempo following as shaky start to the game, the Cape side began to look increasingly dangerous in attack and were close to scoring after 20 minutes when Siyabulela Songwiqi pulled a drive just past the far post.
Tshepo Motsoeneng had his first piece of real action in the 23rd minute when he did really well to save from Lennox Bacela, who was on the end of Phenyo Mongalo's cross.
Mongalo had been having a good game, but was at fault for Santos' opening goal in the 29th minute as he brought down Siyabulela Songwiqi inside the box.
The former Bay United and Kaizer Chiefs winger rifled home from the spot to make it 1-0.
The Peoples' Team were further ahead 20 minutes after the restart when Vuyisile Wana's low angled shot wrong-footed Tignyemb.
Celtic replied quickly as they got themselves back into the match five minutes later when Clifford Mulenga showed good skill to slide in at the back post to convert Mongalo's driven cross.
Santos had to do some serious defending late on as Clinton Larsen's side gave their all in search of an equaliser, but some tenacious tackling and the odd bit of luck saw them over the finish line.