We're told NFL security was notified several hours before kickoff that police were looking for the 26-year-old running back, but the parties essentially came to an agreement that Kamara would be allowed to play in the game, and cooperate with authorities afterward.

"We got in touch with NFL security about 10 o'clock in the morning and let them know that [Kamara] was a suspect in the case and they located him and he was already on the field," Assistant Sheriff John McGrath told the Nevada Current.

He continued ... "So they contacted him and he agreed to meet with us after the game. And so that's just the way we did it since he was cooperating."

Kamara played ... catching 4 passes for 23 yards.

Waiting to make the arrest seemed to payoff for the police.

After the game, police Mirandized the Saints star at Allegiant Stadium ... where he then spoke with investigators, and gave his side of the story.

Kamara admitted he punched the alleged victim at least 1 time early Saturday morning inside a Vegas hotel after he claims a man made a disrespectful comment to someone in his group.

However, the alleged victim tells a different story. He claims Kamara pushed him for an unknown reason, before Alvin and his 3 friends beat the man down.

Cops say they reviewed surveillance video and the footage showed Kamara punching the man at least 8 times.

Kamara was arrested on 1 count of battery w/ serious bodily injury, a felony.