The Grammys are underway and their MC, Trevor Noah, was on a roll in avoiding just about every controversy in the biz in his opening remarks ... except Will Smith, of course.

The ceremony kicked off Sunday in Vegas with a performance by Bruno Mars and Anderson .Paak -- after which, things went indoors at the MGM Grand Garden Arena ... where TN popped up again and start delving into his monologue seamlessly.

He intro'd all the big names who were in the building -- going through a list that included the likes of Justin Bieber, Lady Gaga, Billie Eilish, Olivia Rodrigo and more -- and said the night was going to be a smooth ride where they'd be singing, dancing and giving out awards.

Then came the dig ... "We're gonna be keeping people's names out of our mouths." That, he said, would help keep the night chill ... and the audience laughed it up as a result.

No name-dropping here, but it's obvious what Trevor was referring to ... that is, Will telling Chris Rock to keep Jada Pinkett's name out of his mouth during last weekend's Oscars ceremony -- this after smacking him across the face on stage, live on television.

It's interesting that Trevor went there -- albeit, lightly and not nearly as brutal as he could've been -- because the dude was seen embracing Will at an afterparty last week ... following a long chat they shared.

Seems like he struck a good balance between addressing it and sparing Will further humiliation. Dude's been getting both criticized and ridiculed in the wake of the hit.