Opting to bat first, the visitors lost their talisman AB de Villiers in the very first over but du Plessis struck an unbeaten 79 off 61 balls to power the Proteas to 148-4.
Their bowling attack contained more firepower than Bangladesh could handle and the Proteas shot out the hosts for 96 inside 19 overs to cruise to an easy victory.
"It's the beauty of the team," du Plessis, adjudged player-of-the-match, said in a pitchside interview.
"We've got world class players like AB but we don't rely on one. There are so many other players in the team who can be match-winners."
Arafat Sunny gave Bangladesh a rousing start, dismissing de Villiers in the very first over and the left-arm spinner sent back JP Duminy as well as South Africa kept losing wickets regularly to find themselves in trouble.
Du Plessis hit eight fours in his unbeaten knock and found an able ally in Rilee Rossouw (31 not out), adding 58 runs with him in 6.4 overs to take the team close to the 150-run mark.
Defending the total, the South African spinners got more purchase from the wicket and did not allow any partnership to prosper, frustrating the hosts who were hoping to replicate their limited-overs form having beaten Pakistan and India in recent home series.
Kyle Abbott dismissed Tamim Iqbal in the first over to draw first blood and the hosts capitulated, failing to withstand the relentless hostility.
Shakib Al Hasan topscored for them with 26, while debutant Litton Das managed 22 as only three Bangladeshi batsmen managed double digits.
Duminy, David Wiese and Kagiso Rabada claimed two wickets apiece for South Africa.
"Our batters played too many shots but it's not a worry. We can fix it in the next match," Bangladesh captain Mashrafe Mortaza said.
The teams return to Mirpur's Shere Bangla National Stadium for the second Twenty20 on Tuesday.
(Reporting by Amlan Chakraborty in New Delhi; editing by ...)
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