Its debatable whether that made him a star - I only remember him in small self-parody roles like a poor man’s latter day De Niro - but he certainly made the movie.
Ted Danson as the tap dancing DA in Body Heat.
John Wayne in Stage Coach, although he had title role billing after Claire Trevor. It catapulted him from B-movie singing cowboy (yes, really) to stardom.
As for Harrison Ford, I’d nominate American Graffiti, where he was in a supporting role, rather than Star Wars, where he was one of the stars.
Humphrey Bogart got his big break playing Duke Mantee in The Petrified Forest. Top billing for that film went to Leslie Howard and Bette Davis, but Bogart stole the show.
Mickey Rourke also made the most of his small role.
Add Thomas Mitchell, who played Scarlett O’Hara’s father in Gone With the Wind in the same year, but got his Oscar for Stagecoach.
Speaking of Mickey Rourke, how about the cast of Diner:
Steve Guttenberg
Daniel Stern
Mickey Rourke
Kevin Bacon
Tim Daly
Ellen Barkin
Paul Reiser
I think it was the Spike Lee Joint Jungle Fever that first got Jackson noticed. He was the cracked-out brother to Denzel Washington’s character and he won the best supporting actor award at Cannes. And he’s been awesome ever since.
Sidney Poitier in The Blackboard Jungle.
Penélope Cruz strikes me as a bit of a complicated case as far as international audiences are concerned. I might even guess that Belle Époque got a bit more such attention amongst such in 1992 than Jamón Jamón, even though both were certainly noticed. But her immediately subsequent films had no impact whatsoever in the English-speaking world. Then there’s the 1997 double-header of Abre los ojos and Live Flesh. Neither were huge English-speaking hits, but, on the latter, Almodóvar was an established major figure on the art-house theatre circuit. That begins to get her some Hollywood work.
But I think it’s All About My Mother in 1999 that really tipped her over the point to where Hollywood got really interested. So the trio of Blow/Captain Corelli’s Mandolin/Vanilla Sky (recognising that that’s a remake of something she’d already starred in) in 2001, in all of she’s at least the second-female-lead. After that bunch of stuff, she’s recognisably a global star.
And his last role was playing Lt Columbo (yes, that one) on stage
Woman On Top was a pretty important movie as far as introducing her to America. But she was the female lead in it.
Salma Hayek in Desperado, although I’m not sure how much of a “supporting” role it was. Best career introduction in movie history. 
Richard Widmark in “Kiss of Death” with the memorable scene of him pushing an old woman in a wheelchair down a flight of stairs.
eas the Ralph Cifaretto character in “The Sopranos” inspired by Widmark in “Kiss of Death”?
I think that J.K. Simmons was relatively unknown before he absolutely killed it playing J. Jonah Jameson in the first 3 Spider-Man movies.
Now he is the lead actor in a string of occasionally amusing insurance commercials. Oh, and he won some kind of award, too. 
I first saw him as a guest star on a Homicide/Law and Order crossover. He then was a recurring character on Law and Order well before Spiderman, IIRC. That was a fairly well-watch show.
You’re right about all of that. He definitely worked a lot before Spider-Man. But he was certainly the definition of a “supporting actor” (although a very good one) until after the Spider-Man movies. And now, of course, he’s much more well-known.
We can quibble about “star” but: Abe Vigoda in The Godfather - from virtual unknown to recognizable and steadily working film and television actor.
He was the male lead of Coal Miner’s Daughter; that’s when i first became aware of him.
Jackie Coogan became a popular juvenile actor after “The Kid” with Chaplin. Of course, he’s remembered nowadays as Uncle Fester.
For a year after “Godfather” Vigoda found himself constantly being pulled over by policeman who looked at him with a “I know his face but where”. Got so he would say “Did you see the Godfather-I played Tessio” and the cop would say that’s where I’ve seen you.