Opener Sibanda struck 44 off 33 balls and Waller hammered 49 off 23 to keep Zimbabwe's hopes alive after the visitors won the toss and elected to bat.
After losing the first two of the four-match series to Bangladesh, Zimbabwe's Sibanda came out firing with stand-in skipper Hamilton Masakadza, putting on 45 runs in the opening stand in just four overs.
Mohammad Shahid, playing his debut T20 for Bangladesh, broke the stand, with Mosaddek Hossain taking a catch at point to dismiss Masakadza for 20.
But Waller, who hit two fours and four sixes, and Sean Williams (32) added 74 runs for the fourth wicket to ensure Zimbabwe did not stall.
Apart from Shahid, a string of other Bangladesh players are making their T20 debut including Mosaddek, all-rounder Muktar Ali and pacer Abu Hider.
Batsman Imrul Kayes has also been brought into the squad, while several others are being rested and batsman Mushfiqur Rahim and pacer Mustafizur Rahman are nursing injuries.
The visitors made two changes for Wednesday's match, with batsman Sikandar Raza and bowler Tendai Chisoro replacing Neville Madziva and Wellington Masakadza.
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