It's all in new police video, obtained by TMZ Sports, which reveals Kazee name-dropped his two superstar teammates after he was pulled over in the Dallas area back on Oct. 19 at around 3 a.m.

In the footage, a cop can be heard telling Kazee he had stopped him due to his failure to use a turn signal as well as some erratic driving.

Kazee -- who seemed to be slurring his words -- said "my bad" ... and then explained he had been with the Cowboys' quarterback and running back earlier in the evening.

"I was just with Ezekiel Elliott and Dak Prescott and we were just having fun -- went out," Kazee told the cop.

The 28-year-old, who just signed with the Cowboys this offseason, told the officer he had "probably like three shots" while out -- adding that he, Prescott, Elliott and others were at a restaurant in downtown Dallas.

"Today we was just going out to eat," Kazee said, "because it's rookie night."

The cop then put Kazee through some field sobriety tests -- and you can see in the video, Kazee didn't appear to ace any of them.

Kazee seemed to struggle to count backwards and didn't walk cleanly in a straight line -- and he was eventually arrested and booked on a misdemeanor DWI charge.

Kazee addressed the situation with Dallas reporters a few days following the incident ... saying, "I apologized to my family, my teammates, my coaches and to the owner, who gave me a job."

"I'm happy the Lord helped me get out," he said, adding that he'd "deal with" any punishment the NFL levied on him over it all. "I didn't hit nobody, I didn’t hurt myself. Just thankful I’m here now."