KK was in the Big Apple Monday for the Wall Street Journal Magazine's 2021 Innovator Awards, which was honoring her -- among others -- for her SKIMS line ... something for which she actually wore SKIMS on SKIMS to accept, and which actually helped her out during a fashion snafu.

On the way into the Museum of Modern Art -- where the festivities went down -- Kim showed off a mocha leather dress that covered her curvy figure ... an outfit that's actually part of her upcoming SKIMS line with Fendi.

She looked great, of course, but it sounds like there was a wardrobe malfunction while seated at her table. One of her zippers came undone, and required some relinkage courtesy of her designer, Kim Jones ... plus others, like Demi Moore, who were on hand to assist.

Once Kim got to the podium ... she acknowledged the hiccup, saying thank god she was wearing SKIMS undergarments underneath -- otherwise this woulda been a different kind of show. Pretty funny -- once again proving Kim's got some comedy chops.

She posed with Demi, Lewis Hamilton and others who were also got awards that night -- and on her way out, she signed autographs for fans who were waiting for her.

There were paps on the scene as well, but it doesn't appear too many people were asking the one burning question on everyone's mind ... what's up with Pete Davidson???

As you well know ... she was seen hanging out with Pete -- plus a bunch of other friends -- in L.A. over the weekend, where they were riding rides and having a ball. She also held hands with Pete at one point, and seemed to be partnered with him during a lot of their coaster trips.

We've been told they're just friends, but the fact is ... she's now back on his turf in New York. Might be mere coincidence for what she was there to do, but it is interesting timing, no doubt.