New Zealand were bowled out for their lowest Twenty20 total of 60 in 15.3 overs in the final match of the group played at Zahur Ahmed Chowdhury stadium.
Left-arm spinner Rangana Herath took a career best 5-3 in a destructive spin bowling display of 3.3 overs.
Sri Lanka were bowled out for a paltry 119 in 19.2 overs with left-arm paceman Trent Boult taking a career best 3-20 and Jimmy Neesham 3-22.
Sri Lanka will play the first semi-final on Thursday, against the winners of final group two match between Pakistan and defending champions the West Indies to be played in Dhaka on Tuesday.
India face South Africa in the second semi-final, also in the Bangladeshi capital on Friday.