Victory allowed the Proteas to avenge a shock T20 loss to the same opponents last weekend.
Steady rain restricted play to just the final session on the fourth day.
Bavuma's determined 86 and a more enterprising 78 from de Zorzi were linchpins in the Proteas' effort on a benign surface offering little for the bowlers but also made free scoring difficult because of its two-paced nature.
Bavuma was not involved in the T20 World Cup in which South Africa were beaten finalists.
Markram hoped that this would be the first of more finals to come, in particular when South Africa host the 50-over Cricket World Cup in 2027.
Markram paid tribute to those who were unable to overcome the hurdle in previous tournaments.
After skittling Afghanistan for 56 at Trinidad's Brian Lara Stadium, the Proteas cruised to their victory target, finishing on 60-1.
The Proteas piled up 194-4 off their 20 overs after being put into bat.
Bangladesh enter the T20 World Cup with a bit of uncertainty as they continue to look for their strongest XI. Experienced opener Litton Das has been out of form of late with an average of 13.16 this year in six matches. Although teammate Tawhid Hridoy is confident that Das will make a strong comeback in the tournament.
CSA chief executive Pholetsi Moseki told the Sport24 website that the composition of the team chosen by Walter was a concern, but added that he and Nkwe agreed that there were "cricket reasons" for the racial balance.
Former South Africa all-rounder Mike Procter, the country’s first coach of the post-isolation era and a stalwart with English county Gloucestershire, died aged 77 on Saturday, his family announced.
Going by the collective outcry of the cricket fraternity around the world, led by former Australia captain Steve Waugh, it seems that the people running the game in South Africa have just landed the final blow in the gruesome murder of Test cricket.
They head into the last-four with a record of seven victories in nine matches, having lost to India and, surprisingly, the Netherlands.
Hendricks was only in the team after captain Temba Bavuma was ruled out through illness.
The toss was scheduled to take place at 2:00pm Bangladesh Standard Time but ended up taking place at 2:30pm.
Having made his ODI debut in 2013, De Kock has represented South Africa in 140 matches so far, aggregating 5966 runs at an average of 44.85 and a strike rate of 96.08. He has 17 hundreds and 29 fifties to his name with a high score of 178 that came against Australia at Centurion in 2016.
England and South Africa go into Thursday’s final Test at The Oval without key batsmen as each looks to secure a series that is intriguingly poised at 1-1 after emphatic victories by both sides.
Shane Dadswell, a South African student, smashes 490 not out in a limited-overs club match.
Pakistan Cricket Board (PCB) chairman Najam Sethi says that they are planning to invite Bangladesh and Pakistan next year.