Rylance received the first award of the night at New York City's Radio City Music Hall, for best featured actor in a play - his third Tony for playing the countess Olivia in Shakespeare's Twelfth Night.
The actor, who previously won for Jerusalem and Boeing-Boeing, was also nominated for best lead actor honours for his evil title character in Richard III.
Okonedo won the best featured actress in a play Tony, for A Raisin In The Sun. "I am loving it on Broadway," she said, thanking producer Scott Rudin for believing that a "Jewish, Nigerian Brit" could play the iconic role of Ruth Younger. The show also won best play revival.
A Gentlemen's Guide To Love and Murder, in which a poor man comically eliminates the eight heirs ahead of him for a title, won the best musical award. It had opened rather quietly but had a steady increase in interest, peaking with its huge win over Disney's Aladdin and the built-in love of Carole King songs from Beautiful - The Carole King Musical.
"The little engine that could, did," said an ecstatic lead producer Joey Parnes. The show nabbed a total of four wins, including best book of a musical.
Audra McDonald became Tony's most decorated actress, while Bryan Cranston won a best actor trophy for his Broadway debut. Neil Patrick Harris took home best actor in a musical after years of handing out the awards to others.
McDonald won her sixth Tony for portraying Billie Holiday in Lady Day At Emerson's Bar & Grill, putting her ahead of five-time winners Angela Lansbury and the late Julie Harris for the most competitive wins by an actress. Among those she thanked were her parents for not medicating their hyperactive child.
The latest win - for best lead actress in a play - also makes McDonald the first grand-slam performance winner. She previously won as best featured actress in a play (A Raisin In the Sun and Master Class), best lead actress in a musical (The Gershwins' Porgy and Bess) and best featured actress in a musical (Ragtime and Carousel).
Cranston - in a role far from TV's chemistry teacher-turned-meth kingpin Walter White in Breaking Bad - won the best lead actor in a play Tony for playing former President Lyndon Johnson in Robert Schenkkan's All The Way, which also was crowned best play.
Jessie Mueller beat some strong Broadway veterans in Sutton Foster, Idina Menzel and Kelli O'Hara to take home the best actress in a musical Tony for playing the title character in Beautiful: The Carole King Musical.
Hugh Jackman, back as host after a nine-year absence, kicked off the show with a bounce, hopping up and down like a kangaroo during his opening number.
The best featured actress in a musical Tony went to Lena Hall in Hedwig And The Angry Inch, playing a woman who dresses as a man and plays Harris' boyfriend. The show later won for best musical revival.
Darko Tresnjak won for directing A Gentleman's Guide and the musical also won for best book of a musical and costumes for a musical. Away from the cameras, the now-closed musical The Bridges Of Madison County won for best score and best orchestration.
Kenny Leon won his first Tony for directing the revival of A Raisin In The Sun.
James Monroe Iglehart, who plays the manic Genie in Aladdin, won for best featured actor in a musical and could barely contain his glee as he thanked a long list of people that included God and his wife.
Some 870 Tony voters - members of professional groups such as the Wing, the League, Actors' Equity Association, the Dramatists Guild and the Stage Directors and Choreographers Society - decided the final 26 competitive awards.
Wicked, which is celebrating a decade on Broadway, had its current Glinda and Elphaba sing For Good, and there were songs from two shows that have yet to arrive: Sting performed from his musical The Last Ship and Jennifer Hudson sang from Finding Neverland, the musical about Peter Pan.
This year, Broadway producers have a reason to party. The season's box offices hit a record total gross of 1.27 billion dollars (£755m) - up from 1.13 billion (£672m) the previous season - and attendance was up 5.6% to 12.2 million.