Stuart Binny (25) and last man Umesh Yadav (0) were at the crease when heavens opened up again at the Shere Bangla National Stadium.
India skipper Suresh Raina had won the toss and elected to bat first.
India have already taken an unassailable 2-0 lead in the series after humbling the hosts by 47 runs via D/L method in the rain-truncated second ODI.