Bonus points if the lyrics cite both title and artist.
I can think of three off the top of my head, but I’ll start with just one:
Shooting Star, by Bad Company:
mmm
Glass Onion by the Beatles refers to five other Beatles songs in the lyrics: Strawberry Fields, I am the Walrus, Lady Madonna, Fool on the Hill, and Fixing a Hole.
Rock and Roll Heaven, The Righteous Brothers, mentions six songs.
Johnny Winters’ “Summer Rain” mentions “Sergeant Pepper’s Lonely Hearts Club Band”.
Hootie and the Blowfish’s “Only Wanna Be With You” not only references Dylan’s “Tangled Up In Blue” but lifts an entire verse from Dylan’s “Idiot Wind” off the same album.
Thunder Road by Bruce Springsteen:
mmm
I thought this would be one of the first mentioned, Lynyrd Skynyrd’s “Sweet Home Alabama”:
“Well I heard mister Young sing about her,
Well, I heard ole Neil put her down.
Well, I hope Neil Young will remember,
A Southern man don’t need him around anyhow.”
Ok, it doesn’t specifically include the lyrics or title, but it’s still a clear reference.
My personal favorite is way more obscure. The band Saga did an eight chapter, well, saga, spread across their first four albums (and yes, I know that there have subsequently been more chapters on later albums). The last (at that time) chapter, “No Stranger (Chapter VIII)” featured actual cuts from the previous seven songs.
For that matter, Lennon’s anti-McCartney rant “How Do You Sleep” has the line “The only thing you done was yesterday/And since you’ve gone you’re just another day”–a reference to the Beatles’ “Yesterday” and McCartney’s “Another Day”.
Which was mentioned in Kid Rock’s “All Summer Long.”
Dire Straits’ Romeo and Juliet:
“There’s a place - for us. You know, the movie song.”
Refers to a song from West Side Story
American Pie and Garden Party probably have multiple references each, but offhand I remember the first mentioning 8 Miles High and Helter Skelter, and the second Johnny B Goode. But they are incorporated into the lyrics, not mentioned as songs per se, so I’m not sure if that’s what the OP is looking for.
“The Band Played Waltzing Matilde” by The Pogues.
A similar song (theme wise, anyway), Night Shift, mentions Higher and Higher by Jackie Wilson.
Another semi-mention (obvious reference, but not specifically as a song) is Georgia on My Mind in Back to the USSR.
One of my favorites is Tom Paxton’s When Annie Took Me Home
Rafters rung, songs were sung
Like Spanish is the loving tongue
Ribbons on my life were hung
When Annie took me home
“Spanish is the Loving Tongue” is a Dylan song.
Actually, it does specifically include the title. The reference is to Neil Young’s song Southern Man.
“The Spirit of Radio” by Rush references “The Sound of Silence.”
“Yer Blues” by the Beatles has the line, “Feel so suicidal, just like Dylan’s Mr. Jones.” Which is a reference to Bob Dylan’s song “Ballad of a Thin Man.”
Fairy Tale of New York by the Pogues mentions 2.5 songs:
Ben Folds Five’s song “Kate” says “She plays ‘Wipeout’ on the drums”
The Musical Box by Genesis
“Old King Cole was a merry old soul
And a merry old soul was he;
He called for his pipe, and he called for his bowl
And he called for his fiddlers three.”