The win Saturday gives Montenegro, the 2012 European championship runners-up, five points from four Group B matches.
Nicolae Diaconu scored three goals for Romania, which has two points from four matches and only slim hopes at this point of advancing to the quarterfinals.
Montenegro plays Britain in its final preliminary stage game Monday, while Romania closes against gold medal-favourite Serbia.
The men's field is broken into two groups of six teams. The top four from each group advance to the quarterfinals.