The visitors resumed with Rudolph on 13 and Jacques Kallis looking to add to his total of 107.
Kallis combined with Graeme Smith for a third-wicket stand of 200 runs on day three to put the visitors in a commanding position but could not build on his impressive innings, holing out to mid-wicket for 113.
Rudolph was lucky to still be at the crease after he was given a reprieve late on day three when the Umpire Decision Review System suggested enough of the ball had pitched outside the line of leg stump.
Rudolph made the most of that escape, getting himself set at the crease before lifting the tempo after the lunch break. He slashed a cut shot through backward of point to move to 99 and swept Daniel Vettori to the square leg boundary to raise the milestone. The declaration came shortly after.
New Zealand suffered an early setback when Martin Guptill (6) was undone by a superb ball from Vernon Philander which nipped away and took the edge.
Rob Nicol weathered some torrid bowling as he battled hard to find his touch. He took the ball on the body and looked a bit like he was fending off over-sized wasps on his way to 19 from 71 balls.
But it was all for nothing with the right-handed hitting a full toss from Imran Tahir straight to Graeme Smith at mid-on - a shot which was the very definition of disappointing.