England were 208 for five in their first innings at the close of play at Lord's, trailing by 101 runs, thanks to Bairstow's 72 not out.
It was the Yorkshire batsman's highest test score in his fourth match. Matt Prior was also unbeaten on 22.
South Africa were earlier bowled out before lunch for 309. Number eight Vernon Philander made a test-best 61, the same score team mate JP Duminy registered on Thursday.
Bairstow, who only returned to the team because of Pietersen's controversial omission for sending "provocative" texts to the opposition about his own team, batted with maturity to rescue England after they had slumped to 54 for four.
Ian Bell hit a battling 58 and put on 124 with Bairstow for the fifth wicket.
"He certainly showed some great character, having been left out of the team and having to go away and work on a few areas," Bell told reporters.
"He was tested with (short balls) straight away ... and I thought he handled himself brilliantly. He had obviously worked really hard on a method back at Yorkshire."
Bairstow showed courage in adversity for almost four hours, especially after having looked vulnerable against short-pitched bowling against West Indies earlier this year.
He reined in his natural attacking game early on while consolidating with the equally watchful Bell.
Bairstow then hit leg-spinner Imran Tahir for 13 in one over, with three boundaries through the mid-wicket and mid-on area, before raising England's 100 with a pull for four off Morne Morkel.
Bell scored his first boundary from his 41st delivery, emphasising his patience and the accuracy of South Africa's bowling.
The experienced batsman's patience eventually deserted him when he chased a wide ball from Philander and gave Alviro Petersen a catch at third slip. Bell was furious with himself, slamming his bat into his pads.
England earlier lost their first four wickets in quick succession.
Andrew Strauss (20) was bowled - to the last delivery before lunch - by a Morkel ball that cut back through the gate off the Lord's slope.
It was the ninth time Morkel had accounted for the England captain in 12 tests. No bowler has dismissed Strauss more.
Jonathan Trott was lbw to Dale Steyn for eight but only after umpire Kumar Dharmasena's original 'not out' decision was overturned. Replays showed the ball would have hit leg stump.
The total was then 38 for two and it soon became 39 for three when Alastair Cook played an uncharacteristic, wild slash to a wide ball from Steyn that he edged to Jacques Kallis at second slip.
Steyn had two for 19 in that fruitful six-over spell.
James Taylor (10) also failed to stay at the wicket for long, nicking Morkel low down to Graeme Smith at first slip.
Earlier, England fast bowler Steven Finn claimed four for 75 while wicketkeeper Prior picked up five catches and a stumping.
"It was satisfying to bail the team out, it was a proud moment for me," said Philander. "My game is usually to take it to the bowlers most of the time but I had to adapt according to the conditions of the game.
"The wicket is good to bat on but a bit slow. So the way the guys have bowled has been phenomenal. Bell and Bairstow batted well but if we can take another couple of quick wickets in the morning we are well in the game."
South Africa will leapfrog England at the top of the world rankings if they avoid defeat here.
