The Springboks were made to pay for spurning early shots at goal in their Brighton beating, but this time Handre Pollard took the points and Pietersen scored an opportunist try for a 17-6 half-time lead.
South Africa ruthlessly applied the pressure thereafter, with scrum-half Fourie du Preez outstanding in dictating the tempo.
Pietersen scored two more tries, Schalk Burger was rewarded for an impressive personal performance with a score, replacement hooker Schalk Brits touched down and Bryan Habana added a sixth.
Pollard finished with 14 points, while Michael Stanley's two penalties were all Samoa could muster in reply.
South Africa next play Scotland and the United States - sides who meet in Leeds on Sunday - and could yet top the pool and claim a more favourable quarter-final draw with two wins.
Samoa next play Japan, eager to respond from a defeat where their intent was stated from the start, with the physicality epitomised by flanker TJ Ioane's bone-crunching tackle on Springbok hooker Adriaan Strauss.
The Pacific Islanders were competitive at the breakdown and in the tackle, but were undone by their inability to relieve pressure, some indiscipline and Stanley's inaccuracy with the boot.
Pollard kicked a second-minute penalty and South Africa showed their forward supremacy from the restart, driving Samoa backwards.
Stanley kicked two penalties, but the fly-half's lofted pass was next anticipated by Pietersen, who plucked the ball from the air and raced 50 metres to score.
Pollard dragged the conversion wide, but kicked three more penalties to extend the Springboks' advantage to 11 points.
There was a minor flare up involving Alesana Tuilagi after Eben Etzebeth's fine defence, before the former Leicester winger was caught round the neck by Pietersen after chipping over his opposite number.
Pietersen avoided a yellow card, but Stanley was short and wide with the penalty attempt from his own half.
Willie le Roux, who had a first-half score ruled out for a foot in touch, fumbled forwards in collecting a kick in the opening seconds of the second half as South Africa resumed on the attack.
They did not have to wait long for Pietersen to claim another simple score as, after Samoa were squeezed back up front, the wing completed the overlap.
Stanley missed more two penalties, before being replaced by Tusi Pisi, but momentum was already with the Springboks.
Burger crashed through two tackles to score a third try. Pollard's conversion hit the post.
Cracks appeared in the Springboks defence, but they were reprieved when the Television Match Official spotted a forward pass from Tim Nanai-Williams to Kahn Fotuali'i, ruling out what would have been a fine score by Pisi.
Le Roux was again denied in the corner by Paul Perez's covering tackle as the Springboks chased a fourth try and with it a bonus point.
But replacement hooker Brits emerged with the ball after a rolling maul from a lineout as the Springboks claimed the score they were looking for.
Pietersen again touched down out wide and Habana raced around a tired Samoa defence late on.
Replacement Pat Lambie converted as the Springboks ensured their World Cup campaign was back on track, only marginally spoilt when a pitch invader in a South Africa jersey came on.
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