Paskalis was born in 1929 and studied piano at Athens Conservatory before training as a singer. He sang in the chorus of Greek National Opera prior to making his principal debut there, as Rigoletto, in 1951.
Paskalis sang all his roles in Greek until he was heard by a Viennese agent singing Oreste in an Athens performance of Gluck's Iphig_nie en Tauride in 1958. His first performance abroad was his Vienna State Opera debut later that same year, as Renato in Un ballo in maschera, opposite Birgit Nilsson and Giuseppe di Stefano and conducted by his compatriot, Dmitri Mitropoulos. In a recent interview he called the performance "a great challenge for me, not least in linguistic terms."
Paskalis gave over 600 performances at the Vienna State Opera, including most of the major Verdi baritone roles, as well as Escamillo, Sharpless, Scarpia and Alfio in Cavalleria rusticana.
Following his June 1964 Glyndebourne debut, the London Sunday Times wrote, "This new Macbeth production ... is unique thanks to one artist's genuinely brilliant performance: Kostas Paskalis in the title role. His baritone is of seemingly endless power, remarkable continuity and precision. Here is a voice that contains metal, and its owner knows how to use it artistically and tastefully, with sensitivity and intensity alike. It exudes a nobility bordering on the divine ..."
He made his 1969 debut at Covent Garden as Macbeth, which he called one of his favorite roles. He later performed Iago, Rigoletto and Scarpia at the Royal Opera House.
Paskalis originated the role of Pentheus in the 1966 world premiere of Hans Werner Henze's Die Bassariden (The Bassarids) at the Salzburg Festival. He later sang in the opera's premiere (in Italian) at La Scala in 1967-68, but when The Bassarids had its first performances in English later that season, at Santa Fe Opera, he declined to perform the role in a third language, according to Opera News.
Paskalis focused his career in Europe, although he did sing with San Francisco Opera (Iago and Scarpia), New Orleans Opera Association (Scarpia and Nabucco) and Houston Grand Opera (Iago), and was Alfonso in the 1965 Carnegie Hall performance of Donizetti's Lucrezia Borgia. Paskalis made his Met debut in 1965, as Don Carlo in La forza del destino and later sang Ford in Falstaff, Valentin in Faust and Figaro in The Barber of Seville at the house.
From 1988 _90, Paskalis was artistic director of Greek National Opera, an endeavor which later led him to criticize the Greek government's lack of support for opera and classical music.