A second successive 67 ensured a 21-under-par total of 267 at The Els Club Copperleaf in Centurion for the 30-year-old Van der Walt.
He finished two ahead of Fichardt, who won the Africa Open in East London two weeks ago. De Jager was third, a further shot back after a final-round 69.
Van der Walt, who has a world ranking of 436 and whose only previous success had come on the satellite tours in north America, broke a four-way tie going into Sunday's final round.
He and Fichardt kept up their battle for the lead, but the other overnight pace-setters Charl Coetzee and Mark Tullo of Chile quickly faded from contention. Coetzee hit 72 to finish in joint fifth, but Tullo slumped to a 77.
Van der Walt's eagle at the par-five fourth set him on his way, followed by two birdies in the next three holes that allowed him to get his nose ahead and keep it there.
Fichardt began with three birdies in his first five holes of the day, but then could not keep up with the burly Van der Walt.
Former Ryder Cup captain Jose Maria Olazabal finished bottom of the post-cut field after a final round 75 ensured he finished three over.
The Tshwane Open was the last of six European tour events in South Africa - five of which were won by home golfers.