Australia were 54 for two at lunch on Monday. Hayden was caught at third slip by AB de Villiers off Makhaya Ntini in the third over before a run had been scored.
Australian captain Ricky Ponting made 20, including a four and a hooked six off Ntini, before he was caught by wicketkeeper Mark Boucher from an inside edge off South African captain Jacques Kallis.
Michael Hussey, who opened with Hayden in the absence of the injured Justin Langer, was undefeated on 19 at lunch, after surviving strong leg before wicket appeals by Andre Nel, before he had scored, and Shaun Pollock when he had five.
Both appeals were turned down by umpire Steve Bucknor. He also survived an appeal for a catch behind off Ntini's bowling when he had 19, with umpire Tony Hill giving him not out.
Nel bowled two overs before leaving the field suffering from gastric illness which had been treated with a drip before play. He did not return before lunch.
Langer, who was concussed by a ball from Ntini Saturday, was not at the ground at the start of play. Although it seemed unlikely he would bat, a team spokesman said there was ongoing assessment of his condition.
Earlier, South Africa were bowled out for 258 in their second innings with fast bowler Brett Lee taking both wickets to finish with three for 57.
Boucher took his score from 55 to 63 before he was caught behind by Adam Gilchrist.
He survived an appeal for a catch behind the wicket off the fourth ball of the day, before South Africa had added to their overnight total of 250 for eight.
He top-edged the next ball just over Gilchrist for four when he swung at a short delivery from Lee.
Another top edge from Boucher deflected to Gilchrist and Ntini was bowled two balls later. It took Australia 13 minutes and 15 balls to wrap up the innings. Australia won the first two matches of the series.