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.
South Africa's planned T20 Global League has been postponed for a year, which could leave a raft of players seeking compensation.
South African fast bowler Morne Morkel is likely to be out of action for about six weeks because of a side strain, team manager and doctor Mohammed Moosajee said on Monday.
South Africa name the uncapped duo of Andile Phehlukwayo and Aiden Markram for next week's first test against Bangladesh in Potchefstroom, with the latter to make his debut as an opener.
South Africa and India are believed to be close to an agreement on a schedule for a tour of South Africa in January and February.
Former South Africa players Herschelle Gibbs and Ashwell Prince have slam AB De Villers for his continued absence from Test cricket and insinuate that he is disrespecting his teammates.
Former South Africa batsman Herschelle Gibbs says that the team should hire an Australian who won’t tolerate a ‘buddy-buddy’ kind of attitude.
South Africa captain AB de Villiers insisted his side had done nothing wrong after they found themselves caught up in a fresh ball-tampering row on Saturday as they lost their one-day international series against England.
Former South Africa bowler Lonwabo Tsotsobe has been charged with match fixing and has been suspended immediately after a lengthy investigation, Cricket South Africa said on Monday.
England Lions are set for a clash with Dale Steyn later this summer after his surprise inclusion in one of the South Africa A squads due to arrive in the coming weeks.
Former South Africa batsman Alviro Petersen has been banned from cricket for two years after admitting sitting in on meetings where plans were hatched to fix matches in the domestic Twenty20 competition.