Dallas Cowboys safety Damontae Kazee told a cop he had been with Dak Prescott and Ezekiel Elliott hours before his DWI arrest ... saying he had partied with the two just before getting behind the wheel.

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.