The siblings capped off their five-night residency with an enthralling mix of yet-to-be-released tracks and greatest hits.
“We are all praying that Nick will turn the corner,” the Oscar-winning composer said.
The moment occurred during the band's five-night Broadway residency at the Marquis Theatre.
The Jon M. Chu-directed film adaptation of the popular Broadway musical was originally slated to premiere later next year.
The Apple TV+ series returns to lampoon a new era of musicals later this spring.
The play is currently in previews at The Public Theater in New York City, opening March 15.
The Broadway musical's final performance will come just before the production tours North America.
The "SNL" alums will reprise their roles from the original film.
Once Upon a One More Time will open this spring on the Great White Way.
Rice is the first songwriter primarily known for his work in theater to receive this award since Stephen Sondheim in 1999.