With her best actress award, McDonald became the only woman to win a Tony in all four acting categories. She also tied with the late actress Julie Harris, who also had six wins, including a special lifetime achievement award.
With tears streaming down her face, a trembling McDonald thanked her parents and family and the women who came before her.
"I want to thank all the shoulders of the strong and brave and courageous women that I am standing on," she said. "And most of all Billie Holiday. You deserve so much more than you were given when you were on this earth."
Cranston, a multiple Emmy winner for his role in television's "Breaking Bad," had been a favorite for his portrayal of U.S. President Lyndon B. Johnson in "All the Way," Pulitzer Prize winner Robert Schenkkan's acclaimed play.
"All the Way" was his Broadway debut.
Award-winning Australian actor Hugh Jackman hosted the star-studded ceremony at Radio City Music for the fourth time. The three-hour show included performances by Tony nominee Idina Menzel, music legend Gladys Knight, as well as Alan Cumming and the cast of "Cabaret."
British actor Mark Rylance took home his third Tony, winning for featured actor in a play as the grief-stricken Countess Olivia in the all-male Shakespeare Globe production of "Twelfth Night."
"We would very much like to come back (to Broadway) with some more Shakespeare and we are talking about it but we haven't settled what it will be," said Rylance, who praised the late blacklisted American actor Sam Wanamaker, the force behind the recreation of Shakespeare's Globe Theatre in London.
A flustered and surprised Sophie Okonedo accepted the featured actress prize in her Broadway debut as Denzel Washington's wife in the revival of "A Raisin in the Sun."
Kenny Leon also grabbed the directing prize for the revival of Lorraine Hansberry's acclaimed 1959 play.
"That was shocking and stunning, surprising but I thought the production was well deserving of a Tony Award," he said backstage.
In the musical category, Darko Tresnjak accepted the Tony for best director of a musical for "A Gentleman's Guide to Love & Murder. The satire about a would-be-heir who must get rid of distant relatives to get an inheritance led the nominations with 10 nods.
James Monroe Iglehart, who plays the larger-than-life genie in "Aladdin," jumped up and shouted to loud audience applause after winning the featured actor prize in a musical. Lena Hall nabbed her first Tony for her supporting role in "Hedwig and the Angry Inch."
Forty-four productions, ranging from "Act One," an adaptation of American playwright Moss Hart's autobiography, to "Rocky," the stage version of the Oscar-winning film, opened on Broadway during the 2013/2014 season.
The Tony Awards are presented by the theater industry association The Broadway League and the American Theatre Wing, a not-for-profit organization.