Kenny G Says Kanye's V-Day Gift to Kim Was Last Minute Miracle

Kenny G's living proof any man can whip up an unforgettable Valentine's Day gift for his spouse in the 11th hour, as long as he knows incredibly famous people ... and has incredible luck.

The legendary saxophonist tells TMZ, his V-Day treat for Kim Kardashian West wasn't something Kanye spent months planning out. Instead, he says it all came together the night before.

That's right, Kenny says he got emails from friends of Kanye around 11 PM Wednesday, informing him Ye wanted him to perform for Kim. Fortunately for Kanye, Kenny was in town, happens to live nearby and most importantly ... was stoked to do it.

Granted ... Kanye still had to set up the incredible assortment of flowers.

Mr. G also runs down the songs he picked for the private show and says he was just flattered to be a part of their intimate moment. Sounds like he and Kanye became fast friends, too ... and there could even be a collab coming.

Kenny played it cool when we asked if he got an appearance fee -- but, then he gave us a free show. Soooo ... enjoy!!!