So does Crocodile Rock, by Elton John.
I’m almost positive that there is a song that mentions Sgt. Pepper, but it’s eluding me.
ETA: Oh right, Summer Rain mentioned above, but it was Johnny Rivers, not Winter.
This was the third of three off-the-top-of-my-head tunes I referenced in the OP.
And the song that got me started thinking about this phenomenon.
Here is a cannibalistic example -
Sara by Bob Dylan:
mmm
Veruca Salt’s first hit was a song called “Seether.” In a later, song “Vocano Girls” listeners are informed that Seether is Louise, one of the two singers.
Nerf Herder’s “Van Halen” references several VH songs.
He’s one of those who recorded it, but it was written well before he was born.
The Genesis album The Lamb Lies Down on Broadway has a running theme of song quotes and title references. From memory, there are references to:
“On Broadway” (Drifters)
“In the Mood” (Glenn Miller)
“Blue Suede Shoes” (Carl Perkins/Elvis Presley)
“Runaway” (Del Shannon)
“Needles and Pins” (Searchers)
“It Won’t Be Long” (Beatles)
“Purple Haze” (Jimi Hendrix)
“It’s Only Rock & Roll” (Rolling Stones–distorted into “Knock and Knowall”)
There’s Eddie Money’s Take Me Home Tonight, which actually has Ronnie Specter singing lines from her hit Be My Baby
…which is a reference to “Glass Onion” by The Beatles, which references “Fool on The Hill”, “Strawberry Fields” and “I Am The Walrus.”
Another song that references “96 Tears” is “Human Fly” by The Cramps.
*Well i’m a human fly
it’s spelt F-L-Y
I say buzz,buzz,buzz,and it’s just becuzz…
I’m a human fly and i don’t know why
I got ninety six tears in my ninety six eyes
*
I see that I forgot that “Glass Onion” has already been covered. 
Haven’t seen as good an example as this one in here yet. On Harvey Danger’s ‘Problems and Bigger Ones’, they sing:
It doesn’t make me cry to hear Dylan say,
Most likely you’ll go your own way…
And…
I’ll go mine.
I’ll go mine.
I’ll go mine.
“Punk Rock Girl” by The Dead Milkmen gets the band wrong, but does reference another song:
Actually the Beach Boys did record a version of “California Dreamin’.” Many years after the Mamas & the Papas’ version, of course.
Led Zeppelin mention “The Book of Love” in their song “Rock’n’Roll.”
John Fogerty’s song “Centerfield” mentions Chuck Berry’s “Brown-Eyed Handsome Man.”
Reunion’s “Life Is A Rock (But The Radio Rolled Me)” is just one song or band reference after another.
Here’s just the first verse:
“B.B. Bumble and the Stingers, Mott the Hoople, Ray Charles Singers
Lonnie Mack and twangin’ Eddy, here’s my ring we’re goin’ steady
Take it easy, take me higher, liar liar, house on fire
Locomotion, Poco, Passion, Deeper Purple, Satisfaction
Baby baby gotta gotta gimme gimme gettin’ hotter
Sammy’s cookin’, Lesley Gore and Ritchie Valens, end of story
Mahavishnu, fujiyama, kama-sutra, rama-lama
Richard Perry, Spector, Barry, Archies, Righteous, Nilsson, Harry
Shimmy shimmy ko-ko bop and Fats is back and Finger Poppin’”
Golden Earring’s 1973 “Radar Love”: “Radio’s playing some forgotten song / Brenda Lee’s ‘Coming on Strong’”.
David Bowie’s “Ashes to Ashes” makes repeated reference to his earlier “Space Oddity”.
Buddy Holly’s “Peggy Sue Got Married” is refers back to his earlier hit “Peggy Sue”.
From The Kinks’* Mr. Churchchill Says*:
“As Vera Lynn would say, ‘We’ll meet again someday’.”
Steve Miller’s “The Joker” makes reference to several other songs, mostly his own earlier ones, in its opening verse. It also refers to “The Letter” by The Medallions, as was revealed in one of Cecil’s most brilliant (IMHO) columns. Later in “The Joker” there is also a reference to “Lovey Dovey” by The Clovers.
When my elder daughter first started high school, her school principal was called (and liked to be known as) Steve (not Stephen) Miller. When she first told me this I immediately responded, “Do some people call him the space cowboy?” Of course, she didn’t get it. 
Wow, I don’t know how I could have forgotten this, especially with that blatant reminder in the first reply. The band called Shooting Star have a song called “I Just Wanna Rock” in which all the lyrics (except for the chorus) are basically the titles of well-known rock songs: Shooting Star - I Just Wanna Rock Lyrics
That reminds me of “Vera” by Pink Floyd.
Does anybody here remember Vera Lynn
Remember how she said
That we would meet again
Some sunny day