Lillian Hayman had a showstopper to top all showstoppers in Hallelujah Baby. She won a Tony for her performance. Unlike some of these characters, she had a decently sized role, but that was her her only number.
Along with Carlotta in Follies, I would think that Hattie's Broadway Baby and Stella's song (while a production number (she is the lead and the focus of Who's That Woman) fit the bill.
Also, I think Glinda's solo in the Wiz, Believe, qualifies. I haven't seen it in 45 years (OMG!), but I remember her coming out at the virtual end of the show and stopping the show cold. Dee Dee Bridgewater also won a Tony for this number.
I do agree re the suggestion re Marge McDougall in Promises! Promises!, but with reservations. I think Mercer won the Tony for her comic performance...the song wasn't and isn't much. I don't know why Finneran won a Tony, as she was so over-the-top for my taste.
I don't agree re Bobby in Memphis or in the captain in CFA. Bobby had multiple songs. The captain may have had only one solo, but she played a role in a bunch of the CFA ensemble songs. I also don't agree re Fraulein Kost. She sings a few bars in one song. The role only won a Tony in the original production because there was ZERO competition. Three of the four best musical nominees had no supporting females in the cast. (I Do! I Do!, The Apple Tree, and Walking Happy, which was also a bad musical).
I did not see it, but I seem to recall that Tessie O'Shea won a Tony for one number in The Girl Who Came to Dinner, despite that show's being a mega-flop.