Green’s Dictionary of Slang

(US) to outwit, to win or be superior to another person.

1912–16		in E. Wilson Prelude (1967) 125: upstage: 1919.
1925		(con. 1880s) Wash. Post 25 Jan. SM7: Jargon of the Juveniles Grandma: [...] Up stage.
1935		J. O’Hara ‘Screen Test’ in The Doctor’s Son & Other Stories 161: Well, I used to know her, too. And a whole lot of [stars], so don’t try to upstage me, baby.
1968		P. Barnes Ruling Class II i: The little devil up-staged everybody. He’s a trouper.
1981		(con. 1940s) O’Day & Eells High Times Hard Times 107: Tell the kid to quit upstaging me.
2000		M. Collins Keepers of Truth 89: You didn’t want to upstage Darlene.