Kluivert, 38, was appointed by the Curacao Football Federation (FKK) on March 4 amid confusion surrounding his role.
The FKK initially announced Kluivert as coach of the CONCACAF nation, though it was later confirmed that the Dutchman would assume an advisory position.
And Kluivert, who worked alongside Louis van Gaal as Netherlands finished third at the 2014 World Cup in Brazil, was in the dugout as Curacao edged Montserrat 2-1 at Stadion Ergilio Hato in Willemstad.
Hosts Curacao made a bright start to the proceedings thanks to Papito Merencia, who opened the scoring in the eighth minute.
Lyle Taylor restored parity for Montserrat in the 23rd minute after rounding the goalkeeper, but Curacao were not to be denied victory as Felitciano Zschusschen converted a 39th-minute penalty, despite slipping on the spot.
The return leg will be played in Montserrat on Tuesday.
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