When was the last time an instrumental song was a big hit? (Music Box Dancer in the late 70s?) Seems like ages. Of course I get that “tastes change” but what other explanations might there be?
Axel F from Beverly Hills Cop? '84 or so.
Looks like a bunch of Kenny G from the late 80s and 90s. Apparently, the last top 10 instrumental in the US was his version of Auld Lang Syne in 1999.
I seem to remember Robert Miles’ “Children” being fairly big in the mid 90s, but it looks like it only hit #21 on the Hot 100 (although it did reach #1 on the dance charts.)
That’s a good one. I was thinking “Chariots of Fire” from back in '81. But “Axel F” was a mainstream hit as well.
I’ll trust pulykamell’s more data-driven answer though, you know, if I ain’t heard of it then it must not have been a big deal 
Jan Hammer’s “Miami Vice Theme” hit #1 on Billboard’s Hot 100 in 1985. It was the last instrumental song to reach #1 until “Harlem Shake” 2013.