The 2002 version of "Whisper" has a 1-and-a-half minute long intro from the Romeo and Juliet movie before the song proper.The first 60 seconds have an entirely different composition, with a slower tempo, before jumping to what's more obviously the preamble to the regular song, which goes for around 15 seconds before vocals begin. Evanescence's "Good Enough", from The Open Door, features an instrumental segment on the front of the song.The second one is part of the opening track to the four-song "Concerto for a Rainy Day" suite, starting with "Standin' in the Rain" (again integrated into the first two minutes of the song itself).First is "Believe Me Now", which leads into "Steppin' Out"."Ocean Breakup / King of the Universe" does the same yet again.Ditto with "Secret Messages," from the album of the same title.
"Tightrope" from A New World Record is similar to The Who example above, in that the instrumental is actually the first minute of the track.Also a potential source of terror (at least for the first minute or so). Also "Won't Get Fooled Again" from the same album. The synth riff from The Who's "Baba O'Riley".Similarly, "Fly Like an Eagle" has the separately-titled "Space Intro" using synthesizers.
Steve Miller Band's "Jet Airliner" is preceded by a synth instrumental titled "Threshold".
Interestingly, this is the third track on the album, not the intro.