Ah, thanks for the correction.
Modern lyrics set to classical melodies:
The Toys, “A Lover’s Concerto” (Bach Minuet in G)
The Nice, “Diary of an Empty Day” (Lalo, Symphonie Espagnole)
“Tonight We Love” (Tchaikovsky Piano Concerto #1)
"Full Moon and Empty Arms (Rachmaninoff Piano Concerto #2)
“Stranger in Paradise” (Borodin, Polovetsian Dances)
“And This Is My Beloved” (Borodin String Quartet #2)
Bob Dylan, “Masters of War” (Nottamun Town)
Bob Dylan, “Bob Dylan’s Dream” (Lord Franklin)
Roy Harper, "Naked Flame (Lord Franklin again)
Leon Rosselson, “Battle Hymn of the New Socialist Party” (O Tannenbaum)
Elton wrote the original with Bernie Taupin. He later rewrote the lyrics as a tribute to Diana.
I haven’t heard Foghat’s version of “Honey Hush,” but I can guess what’s going on here.
When The Yardbirds covered Johnny Burnette and the Rock and Roll Trio’s version of “The Train Kept a-Rollin’,” they basically conflated it with the Trio’s version of “Honey Hush,” which came from the same classic Coral album.
In other words, they played the riff from “Honey Hush” (the alternating G down to E) bit, but sang the lyrics from “The Train Kept a-Rollin’” (which does not feature this riff, but rather is a straight I-IV-V progression).
So assuming Foghat covered “Honey Hush” fairly faithfully from the Trio’s version, they’re actually playing the “Honey Hush” riff as they originally recorded it!
It’s The Yardbirds who screwed up…but quite wonderfully so!
The melody from The Carter Family’s “I’m Thinking Tonight of My Blue Eyes” (which may well go back much further than them) was appropriated for:
“The Great Speckled Bird” – Roy Acuff
“Wild Side of Life” – Hank Thompson and the Brazos Valley Boys
“It Wasn’t God Who Made Honky-Tonk Angels” – Kitty Wells
This doesn’t meet the OP’s criterion of exact correspondence, but the song “Miracles” by the country singer Don Williams incorporates melodic elements from Dvorak’s New World Symphony.
Ah, that makes sense! Here’s a YT link of Honey Hush for the curious… (here’s Train) I actually hadn’t heard the Trio’s version (an admittedly astonishing gap in my listening)…going back further, Tiny Bradshaw’s versiondoesn’t really have that menacing feel. Rock n roll took care of that…
Those Rock and Roll Trio sessions are the finest rockabilly, bar none, ever recorded IMHO.
The story goes that Johnny and Dorsey went out and bought a big batch of R&B records in order to cop some tunes for their upcoming album session (to supplement the originals they had already written).
It just so happens that “Train,” “Honey Hush” and “Chains of Love” (another Big Joe Turner song) were in the batch, along with Fats Domino’s “All By Myself.”
The Trio gave each of them their unique stamp (and yes, definitely “menace”!). Each one is a classic that I’ve been performing for 35 years now.
P.S. Tiny Bradshaw, who started it all with “Train,” is from my hometown!
Yep…they were some real gone cats! 
How about from the same artist. I swear Chuck Berry’s School Days is practically the same song as No Particular Place to Go.
Well done on the Rock n’ Roll Trio, DChord…I love their stuff.
I have to run, but I just wanted to chime in and say that Green Day’s 21 Gunshas the same chorus as Bowie’s / Mott The Hoople’s All the Young Dudes.
The bridge from STP’s new single is the same tune as the chorus from Nirvana’s Stay Away. (I personally think it’s an intentional homage to Nirvana, not a “rip-off” as the YouTube poster claims.)
“Amazing Grace” and “House of the Rising Sun” originally used the same tune.
Be a clown by Cole Porter
Make 'em Laugh by Nacio Herb Brown and Arthur Freed.
Cole Porter was the original.
Habanera from Carmen, and Da-doo-ron-ron.
And Carmen Jones, which takes the plot and music from Bizet’s opera, and resets in in 1940’s USA. The bullfighter becomes a boxer.
Boxer Song
Another example – Hank Ballard recycled the melody from his own composition “The Twist” when he wrote ‘Finger Poppin’ Time."
Wow…the Beach Boys had a lot, not just “Surfin’ USA,” but…
“South Bay Surfer” --> “Swanee River”
“Lady Liberty” --> “Lady Lynda” (both their own)
Brian Wilson’s “Someone To Love” --> The Beach Boys’ “San Miguel”
Brian Wilson’s “Desert Drive” --> ELO’s “Don’t Bring Me Down”
As for other artists…
John Lennon’s “Happy Xmas” --> folk song “Stewball”
Paul Simon’s “American Tune” --> a hymn I used to hear in church…damned if I could remember the name!
Willie Dixon’s “You Shook Me” --> Slim Harpo’s “Buzz Me, Babe” --> Slim Harpo’s “I’m A King Bee”
Little Walter’s “Evan’s Shuffle” and Big Walter’s “Honeydripper” are basically the same
Vangelis’ “Chariots of Fire” --> Carey Landry’s church hymn “Abba, Father”
U2’s “Vertigo” --> Coldplay’s “Clocks” --> Ringo Starr’s “It Don’t Come Easy” --> Supremes’ “You Keep Me Hangin’ On”
I remember hearing once that you could take just about every one of Emily Dickinson’s poems and sing them to the tune of “The Yellow Rose of Texas”. Does that count as new lyrics?
You could do her poems to “Gilligan’s Island,” too. That’s not really that unusual, considering she wrote many of her poems in common meter, which is used very often in traditional ballads and hymns.
Forgot a few…
“A Young Man Is Gone” → “Their Hearts Were Full Of Spring”
“And Your Dream Comes True” → “Baa Baa Black Sheep” / alphabet song / “Twinkle, Twinkle Little Star”
“Student Demonstration Time” → “Riot In Cell Block #9”