Melissa Aldana performs at the 2013 Thelonious Monk International Jazz Saxophone Competition at The John F. Kennedy Center for Performing Arts in Washington. (Paul Morigi)

After 26 years, the annual Thelonious Monk International Jazz Competition has become recognized as the world’s most prestigious talent contest for budding jazz musicians. Many young stars have been discovered, but until Monday, no woman had won an instrumental competition.

Among the 13 semifinalists in this year’s contest, which featured the saxophone, there was only one woman, Melissa Aldana, a 24-year-old tenor saxophonist from Santiago, Chile. History was made when she took the top prize at the final competition Monday night at the Kennedy Center’s Eisenhower Theater, beating out tenor saxophonist Tivon Pennicott and alto player Godwin Louis to claim a $25,000 scholarship, a recording contract with the Concord Music Group and a headline appearance next year at the Kennedy Center.

“I’m in shock,” she said in a brief backstage interview after the competition. “I’m really surprised and honored to be here.”

Several women have won the Monk competition as singers, but Aldana, a graduate of the Berklee College of Music in Boston, is the first to win on an instrument. She is also the first winner from South America and is believed to be the first second-generation competitor. Her father, Marcos Aldana, participated in the 1991 saxophone competition, which launched the career of Joshua Redman.

In her performance, Aldana played the standard “I Thought About You” with a slightly breathy tone, bouncing along in a classic swing rhythm while dashing off fast, subtle arpeggios that fell into perfect place. Her second number, an original called “Free Fall,” had bold chord intervals, not unlike a Wayne Shorter tune from the 1960s.

Shorter, in fact, was one of the judges of the competition and was honored by the Monk Institute, a Washington-based jazz education organization, with a lifetime achievement award. A galaxy of jazz stars performed several of his tunes, including singer Kurt Elling, trumpeter Roy Hargrove and saxophonist Branford Marsalis. In a preview of his Kennedy Center concert next week, Shorter took the stage with his quartet to play a brash, angular tune.

There was also a tribute to George Duke, the smooth-jazz jack-of-all-trades, who was the musical director for the Monk competition before his death last month.

In past years, the competition has tended to be overshadowed by a star-laden sideshow with little connection to jazz. The guest performers this year included singer Cassandra Wilson, who spent too little time onstage, and blues-rock guitarist Robben Ford, who spent too much.

Still, the spotlight shone brightest on Aldana, who embodies a new sense of possibility and direction in jazz. After she took part in a closing all-star performance of Jimmy Heath’s “Gingerbread Boy” — with the ageless Heath still in good form — Aldana had one more thing to do. She had to call her dad to tell him she’d just won first place.