Jay Leno’s got Nikki Glaser’s back, and he's not having any of the backlash -- the comedy legend thinks she absolutely killed it during her Golden Globes hosting debut.

In fact, Jay tells TMZ he thinks Nikki's hosting gig couldn't have gone better ... adding to us in L.A. Monday that he thought her performance went off without a hitch, and every joke hit just right.

Check out the full clip where Jay breaks down why every joke Nikki cracked was spot on, walking the edge with enough truth that her targets wouldn't get offended.

As for those Diddy accusers upset about Nikki’s jabs at the disgraced rapper -- Jay's got a clapback about Diddy himself for all of them.

Back to Nikki, it's all sunshine and rainbows -- Jay's been seeing her potential for years, ever since he had her on his talk show. Whether she wants to dominate the late-night circuit or keep the laughs rolling as a comic, he's sure she’s got the chops to do it all.

Also, don't miss the update on JL's injuries from that nasty fall back in November!