Bill Gates got a feeling inside his bones at the Justin Timberlake show christening a new resort in Sin City ... and we've got video of the billionaire dancing his face off to one of JT's hits.

Justin was onstage for the grand opening of the Fontainebleau Las Vegas and Bill was in the star-studded crowd ... dance, dance dancing along to "Can't Stop the Feeling."

Bill looks like he's got that sunshine in his pocket and that good soul in his feet ... and he's moving so phenomenally next to his girlfriend, Paula Hurd.

Other celebs going electric and wavy during Justin's set included former NFL star Rob Gronkowski and his S.I swimsuit model GF Camille Kostek.

Cher was also dancing with her boyfriend Alexander "AE" Edwards ... and Lenny Kravitz was moving and grooving in his seat, a few chairs down from Kim Kardashian, Kendall Jenner and Ivanka Trump.

As we reported, Hollywood flocked to the desert for the Miami landmark's expansion to Las Vegas, gambling and schmoozing inside Jeff Soffer's resort.