By a generous favour of family friends, Jelena and Pavle Riđički von Skribešće, in the year 1850 his musical education started at the Conservatory in Vienna.

He studied harmony and counterpoint, as well as the basic piano lessons, with a court composer and prominent organist Simon Sechter, also the professor of Anton Bruckner.

Among them were the Serbian Patriarch Josif Rajačić, Russian priest and emissary in Vienna Mikhail Fedorovich Raevsky, the Serbian Prince Mihailo Obrenović, metropolitan of Serbia Mihailo and the Montenegrin Prince Danilo I. Stanković started his melographic work in the field of folk songs and bourgeois melodies shortly after his arrival in Vienna.

By harmonizing the great number of notated church melodies for four-voice choir, he left the rich inheritance to his Serbian people: three published books of the Orthodox Church Chant of the Serbian People (Vienna 1862, 1863, 1864 and Belgrade 1994, as a facsimile edition), as well as the 17 manuscript volumes with four part choral settings and five volumes with about 400 pages with traditional church chants from the Octoich, the General and special chant, Festal chants from the Menaia, the Triodion and the Pentekostarion.1 Before Kornelije Stanković, the newly founded Serbian church choirs and musical societies in Austro-Hungary and the Principality of Serbia had compositions of Russian composers and less famous musicians (Gottfried von Preyer and Benedict Randhartinger from Vienna, Francesco and Giuseppe Sinico from Trieste, Weiss von Berenfels from Petrinja) on their repertoire.

With the publication of Stanković's work, new harmonizations of the Serbian chant became eligible for the singers and the conductors of the church choirs from Vienna, Trieste, Zadar, Kotor, Petrinja to Pančevo, Timișoara and Belgrade.

Brief but distinctive activity of Kornelije Stanković as a conductor of the First Belgrade Singing Society (1863–1864) particularly contributed to the affirmation of the Serbian national musical creativity.

As a successor of Milan Milovuk, Stanković made a significant turn over on the repertoire by introducing new harmonized Serbian folk melodies instead of foreign songs.

Besides from arranging and publishing, Stanković also performed his transcriptions of traditional folk and church melodies as a pianist, with his friend, the painter and excellent baritone Stevan Todorović in Vienna, Pest, Buda, Belgrade, Novi Sad, Sremski Karlovci, Sombor, Pančevo, Sremska Mitrovica, Šabac, Valjevo, Kragujevac.

On the initiative of prof. dr Danica Petrović, in 1993 in Sremski Karlovci started the work of the Summer school of church chant "In memory of Kornelije".

Twenty years later (2006), in the organization of the Institute of Musicology SASA, Matica srpska and Academy of Arts from Novi Sad, another, international scientific assembly "Composer and his environment" was held.