The hosts bundled Zimbabwe out for 131 runs in 19.3 overs in a docile wicket before easily reaching 136-6 in 17.4 overs to go 1-0 up in the two-match series.
Waller struck 68 runs off 31 balls as Zimbabwe recovered from a disastrous start to get to a decent score.
Zimbabwe set for Bangladesh one-dayers
Cremer then finished with 3-29, including two wickets in one over, but it was not enough for the visitors to end their dismal run in the tour.
Zimbabwe had lost the preceding three-match ODI series 3-0.
Tamim Iqbal scored the highest for the hosts with 31 runs, while Mahmudullah added an unbeaten 22 to steer Bangladesh home.
Mashrafe Mortaza, unbeaten on 15, hit Luke Jongwe for a straight six to end the game with more than two overs to spare.
Electing to bowl first, Bangladesh skipper Mortaza and alAmin Hossain struck early to reduce Zimbabwe to 10-3 inside three overs before Sean Williams (15) and Craig Ervine (20) offered some resistance.
Bangladesh tour: Zimbabwe to play three ODI, two T20s in November
Waller joined Ervine after spinner Nasir Hossain bowled Williams to leave Zimbabwe tottering at 38-4.
Waller launched an immediate counter attack to take 17 runs off debutant leg-spinner Jubair Hossain’s first over.
He then scored 20 off the next over by Nasir and completed his 50 off just 20 balls, Zimbabwe’s quickest in T20Is.
Waller, who hit a total of four fours and sixes, was eventually dismissed by Mustafizur Rahman as Liton Das took a catch at deep midwicket.
Mustafizur claimed 2-16 while Mortaza, alAmin and Jubair each grabbed two wickets and gave away 20 runs each.
The second match of the series will be held at the same venue on November 15.
Published in The Express Tribune, November 14th, 2015.
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