Openers Gaby Lewis and Amy Hunter put on 34 for the first Ireland wicket, with Lewis first to fall for 14 in the sixth over.
Hunter was out for 23 in the ninth but Prendergast’s contribution off 25 balls and Delany’s impressive knock helped the tourists to a healthy total.
Nahida Akter was the pick of the home bowlers with 2-20.
Wickets fell regularly during the Bangledash response, with only middle order batters Sharmin Akter (38) and Shorna Akter (20) putting up significant resistance.
The pair combined for a fifth-wicket partnership of 48 but by then their side’s hopes of victory were already hanging by a thread.
The hosts’ final three wickets fell within the space of four balls as Ireland triumphed with something to spare.
In addition to Prendergast’s three-wicket haul, Arlene Kelly and Delany took two wickets apiece.
