Lafai, a one-test Kiwis international and former Warriors forward, and fellow Dragons player Dunamis Lui were also allegedly involved in the fight.
Shortly after, Lafai and Havili were stopped nearby and ordered by police to move on.
However police came across them once again, a short time later on Crown St, where they were involved in an altercation with a group of men and were taken into custody.
At Wollongong Police Station where they were issued with infringement notices for continuing intoxicated behaviour after a move-on direction.
Lafai was signed to the Dragons on a two-year deal from Canterbury at the start of the year but had been dropped to reserve grade at the weekend by coach Paul McGregor, after the side's recent string of losses.
The Dragons said they were co-operating with police and had informed the NRL integrity unit.
- AAP