The visitors were 110 for two in their second innings, trailing England by 12 runs, when play was finally called off for the day.
Hashim Amla completed his half century in the morning, reaching 71 not out with 14 fours while Jacques Kallis was unbeaten on two, before rain sent the players in for an early lunch and they did not take the field again.
"We knew we would have to bat well in the second innings," South Africa coach Mickey Arthur told reporters. "I think it's even-stevens now ... there's still a lot of hard work to do.
"The guys will be fighting to win because I still think we have the opportunity to win this test."
Arthur said if South Africa could get 220 ahead "there would be a lot of pressure" on England's top five batsmen.
He added his team's poor first-innings total of 194 was largely due to release of pressure after they took an unassailable 2-0 lead in the series in Birmingham last weekend.
"All the things we'd done so well in the last 18 months we forgot," said Arthur. "That comes down to relaxing a bit mentally."
The win at Edgbaston prompted England captain Michael Vaughan to resign and South African-born Kevin Pietersen took over, scoring a century on Friday in his first innings as skipper.
Arthur said England were impressive, having had a point to prove after losing the series.
"Kevin played really well," he said. "He's got big boots to fill but he's certainly started the right way."
South Africa lost Neil McKenzie for 29 in the morning when he edged a ball from Stuart Broad on to his stumps but the 25-year-old Amla played with confidence.
"He's so calm and he's got such a good head and he's pretty streetwise for his age," Arthur said.
The visitors had resumed on 37 for one after England removed captain Graeme Smith for a duck on Friday.
Amla survived one extremely difficult half-chance when he got an inside edge to a ball from Andrew Flintoff.
Tim Ambrose dived full stretch to his left and got a glove to the ball but failed to hang on. England coach Peter Moores said the keeper did well simply to reach it.
Moores added that Ambrose, under pressure after failing to shine with the bat, had injured the ring finger of his left hand on Friday.
"There's still a lot of cricket to play but we are in a good position," said England's coach.
"We are still ahead and they are two wickets down ... it will be important to come back early tomorrow and put them under pressure."
Moores praised Pietersen's leadership.
"He's kept things pretty simple," Moores said, adding the skipper had told the players he wanted a positive, aggressive approach.