Bangladesh now lead eighth-ranked Pakistan by five points, while it is ahead of ninth-ranked West Indies by 14 points.
Bangladesh completed a five-wicket win over New Zealand after chasing down a 271-run target; Black Caps win tri-series.
Bangladesh still searching for maiden away win against New Zealand.
The left-arm seamer picked up four wickets while the opener hit an unbeaten 87.
Bangladesh will be keen to gain some winning momentum ahead of the Champions Trophy.
South Africa reduces gaps with India to six points, while nine points now separate third-ranked Australia from seventh-ranked Sri Lanka