OK, so for me personally, I wouldn't say it was the very first time, but a game that really stood out and I felt like gaming soundtracks truly reached the quality level of film, had to be Chronicles of Riddick: Escape from Butcher Bay.
Those two are just examples, there are more songs in the game that really shocked me throughout when I played it back on release (and still do today). I think the only other game I can think of that didn't have as much of an impact for me, was MGS2, that had cinematic music as well. For some reason, there were a lot of people at the time, that kept saying the music in this game was the Pirates of the Caribbean theme, that annoyed me.
Edit - I guess I should have asked, what was the first game you noticed a cinematic-ally dynamic soundtrack?