Batting first after losing the toss, Bangladesh HP posted 158 all out in 20 overs before bowling Malaysia out for 69 in 16 overs to seal a comfortable victory.
The hosts made a flying start with the ball as Abu Haider Rony struck with the very first delivery, clean bowling Malaysia opener Nazmus Sakib.
Rubel Hasan then dismissed the other opener in the second over as Malaysia quickly slipped into trouble.
The visitors lost six wickets before reaching 50 runs and never recovered. Ahmed Aqil Wahid top-scored with 29 off 25 balls, while Rubel and Rakibul Hasan claimed two wickets apiece.
Earlier, Bangladesh's top order struggled to build momentum. Jisan Alam was dismissed without scoring, while Ariful Islam made 15. Zawad Abrar briefly steadied the innings with a 28 off 18 balls, but Bangladesh were reduced to 75 for five after 10 overs.
Captain S M Meherob and bowling all-rounder Abdul Gaffar Saqlain then rescued the innings with a crucial 52-run partnership for the sixth wicket.
Saqlain made 32 off 26 balls before falling in the 17th over, while Meherob played a composed innings to guide Bangladesh towards a competitive total.
The bowlers then completed the job with a clinical display, restricting Malaysia to just 69.
The second and final T20I will be played at the same venue on Monday.
