See Photos From the Musical That Nearly Swept the Tonys in 1962

This year’s nominees for the Tony for Best Musical include a love story, a comedy, a revenge story and an adaptation of a graphic novel. Theater critics’ predictions lean heavily in favor of the last on that list, a musical based on Alison Bechdel’s memoir Fun Home. Back in 1962, the contest for Best Musical also had a front-runner, and that show took home nearly all the awards available for the taking. How to Succeed in Business Without Really Trying, based on the book of the same name, won not only Best Musical, but also Best Producer, Author, Leading Actor, Featured Actor, Direction and Musical Direction.

The face of that musical’s success was Robert Morse. He’s probably better known to today’s audiences as Mad Men‘s Bert Cooper, but of all the roles he’s taken on, during a career spanning six decades, his most remembered is How to Succeed’s ambitious J. Pierrepont Finch, a window washer who rises to chairman of the board of the World Wide Wicket Company. Morse, LIFE wrote, “makes unfair play so outrageously funny that he should be hanged in effigy by the Boy Scouts.”

A glimpse at Gjon Mili’s photos of the musical leaves little doubt as to why it collected so many awards. More than half a century later, the energy is still palpable, and Morse’s expressions chock full of, as his character would put it, impetuous youth.

Liz Ronk, who edited this gallery, is the Photo Editor for LIFE.com. Follow her on Twitter @lizabethronk.