Lae metropolitan superintendent Anthony Wagambie Jnr says the first murder occurred at the back road of new block while the other death was caused after a drunken brawl at the bowling club carpark, where his body was found in a nearby drain.
The woman was allegedly raped when relatives of the first victim retaliated, kidnapping her and another male, who were later found by police.
Both incidents occurred between 3 to 4am Sunday.
Police are on the lookout for four suspects who were involved in the death of the first man, all of whom are believed to be from the Wosera district, East Sepik Province.
Meantime, apart from these events, the Lae police boss says Independence in the city was quiet.
He commended the public for their cooperation and acknowledged police personnel for carrying out their duties effectively.
He said when there is cooperation from both the public and police, such major events will flow smoothly.