By 1962, following Ulanova's retirement, Plisetskaya embarked on another three-month world tour. As a performer, notes Homans, she "excelled in the hard-edged, technically demanding roles that Ulanova eschewed, including Raymonda, the black swan in Swan Lake, and Kitri in Don Quixote." In her performances, Plisetskaya was "unpretentious, refreshing, direct. She did not hold back." Ulanova added that Plisetskaya's "artistic temperament, bubbling optimism of youth reveal themselves in this ballet with full force." World-famous impresario Sol Hurok said that Plisetskaya was the only ballerina after Pavlova who gave him "a shock of electricity" when she came on stage. Rudolf Nureyev watched her debut as Kitri in Don Quixote and told her afterwards, "I sobbed from happiness. You set the stage on fire."
In 1962, the Bolshoi was invited to perform at the White House by president John F. Kennedy, and Plisetskaya recalled that first lady Jacqueline Kennedy greeted her by saying "You're just like Anna Karenina."
U.S. Attorney General Robert F. Kennedy, the younger brother to president John F. Kennedy, befriended Plisetskaya, with whom he shared the birth date of 20 November 1925. She was invited to gatherings with Kennedy and his family at their estate on Cape Cod in 1962. They later named their sailboat Maya, in her honor.