Skipper Graeme Smith said South Africa's confidence was growing after they broke a 10-game losing streak by beating Bangladesh at Edbaston.
South Africa bowled the Tigers out for a record low of 93 at Edgbaston before racing to a nine-wicket win.
"I think the team is moving on and getting stronger day by day," said Smith, who hit 42 not out off 52 balls.
"It was important to put a dominant performance in, and we did that with bat and ball. I was pretty chuffed."
The young opening batsman added: "When you're playing smaller teams like Bangladesh it's important to put dominant performances in.
"You can still take confidence out of these wins. So we move onto our quarter-final now against the West Indies with a win under our belts."
Smith was pleasantly surprised when counterpart Rajin Saleh opted to bat first after winning the toss.
"I thought there would be a bit of juice in the wicket and we were definitely going to bowl first.
"But I don't think it did as much as expected and I was impressed with the way we bowled up front.
"We bowled with a bit of aggression, put it in the right areas and got the ball to swing.
"Bar two dropped catches I think it was a very decent day."
Bangladesh never recovered after slumping to 20-4 early on, and opener Charl Langeveldt - one of three bowlers to take three wickets - was named Man of the Match for his 3-17.
The only real negative for South Africa was the failure of out-of-form Herschelle Gibbs, who had his off-stump levelled by Tapash Baisya for four.
"There was a little bit of movement out there, so you can get a decent ball and get out to it," Smith said in Gibbs' defence.
"I think for him it's just about getting to 20 and moving on from there. He is an important cog in our team and it is important he gets runs."
South Africa have employed a team psychologist for their Champions Trophy campaign.
"The mental side of the game is always something we've wanted to work on," Smith explained.