Underage Kylie & Kendall Jenner Hit Sex-Themed 21-And-Over Nightclub -- ILLEGALLY

11:12 AM PT -- TMZ spoke to a manager of the club who insists the bouncers checked IDs at the door … and both girls presented IDs showing them to be 21+.

He tells us … they do NOT know the Jenner girls and did not recognize them as being part of the Kardashian clan.

He also says … club management is very aware that underage celebrities try to drink illegally … so they’re very particular about checking IDs … especially when photographers are outside shooting everyone who goes in.

We’ve contacted the Jenners’ rep … and haven’t heard back.

16-year-old Kylie Jenner and 17-year-old Kendall Jenner went out on the town last night ... partying at Vignette lounge in West Hollywood -- a 21-and-over club, and it appears the club and the girls broke the law.

The club features Wax Rabbit every Tuesday night, featuring what the club calls "a new, voyeuristic, hip hop and nudity nightclub experience."

So the burning question -- how did Kylie and Kendall legally get in the club. We did some digging, and found the ONLY exception to the 21 and over law is if the underage person is employed as a musician, but the musician must be 18 minimum. Neither girl is 18.

An official for the Dept. of Alcoholic Beverage Control tells TMZ ... both the girls and the club appear to have broken the law and could have been cited had they been caught in the act. The official tells TMZ his Dept. may launch an investigation.

And it gets worse ... Even if the girls were 18 and there as musicians, they wouldn't be allowed in if there was any nudity, and the club often features topless dancers on Wax Rabbit night.

BTW ... on their way out, the girls were shielded by blankets.

At the end of the night, Kylie and Kendall looked ... tired.