The home team frustratingly lost a wicket in the final over of the day when Takudzwanashe Kaitano (12) edged Corbin Bosch to third slip with Zimbabwe going to stumps on 32-1.
The Proteas started the third day on 49-1 with Mulder 25 not out and Tony De Zorzi on 22 but the latter did not last long, making his way to 31 as seamer Tanaka Chivanga made the breakthrough.
David Bedingham then joined Mulder at the crease and the pair put on a 72-run partnership for the third wicket before Bedingham (35) was caught at mid-wicket off the bowling of left-arm spinner Wellington Masakadza (4-98).
Debutant Lhuan-dre Pretorius, coming off 153 in the first innings, could not repeat his heroics and was bowled by leg-spinner Vincent Masekesa for just four to a ball that turned sharply.
It was 155-5 soon after when Masekesa made a double breakthrough as Dewald Brevis went for a wild swing but saw his stumps castled.
Mulder remained positive throughout the morning session and went to his second Test century, and his first batting at number three, in his 20th match in the last over before the lunch break with the Proteas going to the interval with the total on 185-5.
Mulder and Kyle Verreynne then took their partnership to 104 in the second session before Mulder tried to take on off-spinner Wessly Madhevere but was well caught on the mid-wicket boundary.
It was not long after that wicetkeeper-batter Verreynne edged Masakadza to slip to walk back to the dressing room for 36 as the Proteas were 259-7.
Bosch and Keshav Maharaj then swelled the lead close to the 500-run mark with stand-in captain Maharaj hitting his sixth Test fifty before being bowed for 51.
Bosch fell for 36 before final pair Codi Yusuf and Kwena Maphaka took the lead to 536 before home fast bowler Blessing Muzarabani wrapped up the innings.
Zimbabwe openers Kaitano and Prince Masvaure (5 not out) did well to survive 18 overs but Bosch took the final wicket to make the Proteas go to sleep happier.
Corbin Bosch picked up a maiden five-wicket haul as the Proteas wrapped up a mammoth 328-run victory in the second session of the fourth day of the first Test against Zimbabwe in Bulawayo.
South Africa lead Zimbabwe by 216 runs at the end of Day Two of their opening Test in Bulawayo.
Lhuan-dre Pretorius became the youngest player to score a Test century for the Proteas to help the visitors recover from 55-4 to post 418-9 at stumps on day one against Zimbabwe in Bulawayo.
Lhuan-dre Pretorius, Dewald Brevis and Codi Yusuf will all make their Test debuts for the Proteas against Zimbabwe in Bulawayo on Saturday, stand-in captain Keshav Mahraj has confirmed.
