Jazz has plenty of examples:
Rollins-Saxophone Colossus: "St. Thomas"
Coleman-Shape of Jazz to Come: "Lonely Woman"
Coltrane-Love Supreme: "Part 1"
Brahem, Anour-Thimar: "Badra"
For classical, it is hard to pick favorite opening movements or single movement works, but the following come to mind:
Shostakovich-Piano Trio No. 2
Beethoven-Violin and Piano Sonata No. 5 ("Spring")
Mozart-Vesperae Solennes Confessore
Adams-Violin Concerto