Francis Scott Key
(I mean, who even knows any of his other songs?)
Directly answering “biggest career out of one song” (and not just “biggest one hit wonder”), would have to be Buffet (as a previous poster said).
It’s got a chain of restaurants, margarita mix, tequila, food brand. His company is Margaritaville Holdings LLC
Sure, he had a couple other hits, but “Margaritaville” is an industry.
Come to think of it, he did license “Cheeseburger In Paradise” to a restaurant company, too.
I love this song. For the longest time, it wasn’t available on iTunes, so I dug up an obscure 80s One Hit Wonders compilation just so I could have it on my iPod.
Proof enough of this - I saw them on Late Night with Conan O’Brian sometime in the early 00’s, and they performed BLISTER IN THE SUN!!! BTW, I saw them perform as part of a multiple lineup show in 2001, and they sucked terribly.
True Story - I went to this Halloween Haunt somewhere in Massachusetts when I was in college, which was being advertised as having Boris Pickett as a performer. He did ONE song - Monster Mash! I mean, the guy’s entire career is Halloween songs (It’s Alive is 10x the song that Monster Mash is) so he easily could have done a whole set. I felt ripped off.
The song also gets dragged out for Valentine’s Day and Presidents Day on KBBL 
Henry the VIII wrote Greensleeves. That was pretty much his only hit, and he definitely lived the rock-star lifestyle – scandals, affairs, messy divorces…
I don’t know if he’s made a career out of it. I remember reading that by the end of the same year this song was released, he went back to work at a gas station.
By clicking on his name on that page, I discovered that Greenbaum (performing as Dr. West’s Medicine Show and Junk Band) also charted with The Eggplant That Ate Chicago in 1968.
BZZZT–Wikipedia says that is a legend and probably not true.
Different name on the 45 counts as a separate act 
. And that song (Spirit in the Sky), which I love, has to be on at least a dozen movie soundtracks in the last ten years.
The lead singer on “Tarzan Boy” (GREAT song) died of AIDS in 1995.
Especially since he only wrote the lyrics. They happened to fit an earlier tune composed by one John Stafford Smith.
Iron Butterfly=In the Gadda da vida
One hit wonder that has legs.
The follow-up to “Spirit in the Sky,” “Canned Ham,” didn’t quite crack the Top 40. Yes, the Jewish Greenbaum followed his song about Jesus with a song about ham.
I still don’t think anyone has topped Wayne Newton.
He started life as the son of an auto mechanic in Roanoke, Virginia, got a few performing gigs, managed to get one big hit record under his belt (“Danke Schoen”), used that signature song to propel a long-running career in Vegas, managed to parlay that into part ownership of a casino, continues to have a full slate of shows, and now has a major Boulevard in Vegas named for him.
Hard to top. “Danke Shoen” indeed!
Carl Perkins, “Blue Suede Shoes.” The rest are all pikers.
Hence the Paul Simon lyric “Don’t wanna end up a cartoon in a cartoon graveyard.”
All my suggestions have already been mentioned 
Six on the Mainstream Rock Tracks.
And six albums went Platinum or better.
Another vote for Don McLean and American Pie. It’s exactly what I was thinking when I opened this thread.
I know he has lots of fans but imagine that your only big hit is only one of the best song ever written.
That’s his signature song, but his biggest hit on the singles chart, by far, was “Daddy, Don’t You Walk So Fast.”
Did you mean Springfield (Rick)? Rick claims they are often confused- my guess is, he gets it waaay more often than Bruce does.