Jennifer Lopez -- Crisis Mode After Gig For Alleged Evil World Leader

Jennifer Lopez made a quick buck Saturday putting on a show for one of the world's most repressive leaders ... but it might not have been worth it considering the s**t storm she's in now.

J.Lo's being blasted for putting on a special birthday concert in Avasa for the President of Turkmenistan Gurbanguly Berdimuhamedow -- complete with a serenade of "Happy Birthday, Mr. President".

The reason being -- Gurbanguly's notorious for the widespread human rights abuses in his country: extreme censorship, ethnic repression, utilizing torture etc. Human Rights Watch considers Turkmenistan's gov one of the most repressive in the world.

A rep for J.Lo went straight into damage control today, hoping to take heat off the singer, explaining, "Had there been knowledge of human rights issues any kind, Jennifer would not have attended."

Do celebs not get Google?