Bafana Bafana scored just once in an unimpressive group stage campaign that featured a 1-0 win over Namibia and defeats to Ivory Coast and Morocco by the same scoreline.
The 1996 champions sneaked through in the final qualifying spot reserved for the four best third-place sides, but Baxter is quietly confident the occasion of playing Mohamed Salah's Egypt in front a partisan 75 000 crowd will energise his players.
"The fact that we're playing against the home nation is inspiring," Baxter told reporters on Friday.
"Knowing the Egyptian people, knowing their passion for football, knowing their expectations are very high, knowing that they have some great players, I believe that the pressure would be more on them because for them it would be a national disaster if South Africa beat them, for us it would very disappointing."
He added: "We will go into the game quietly believing that we can cause an upset, but knowing that we will have to play very, very well because this is a good Egyptian team and they will have massive support.
"Maybe one of the jobs that we have to do is to try to quiet the crowd by being a tougher opponent than people think."
Egypt eased into the knockout stages with three wins from three but have yet to hit top gear in their quest for a record-extending eighth Cup of Nations title.
Their record at home in the competition is formidable with three triumphs in four editions as hosts, but Baxter feels South Africa can use the Egyptian support in their favour.
"It's our job to bring maybe some frustration ... if we can do that and the crowd become a little bit impatient, the players will feel that on the field. We know that the home nation can be good thing, but that can be also a big pressure."