Bernard Challandes' side, who were only given UEFA membership in 2016, sit top in Group D3 and will secure promotion and a play-off place if they can avoid a home defeat against Azerbaijan in their final game on Tuesday.
Vedat Muriqi got the Kosovans off to a flying start with a 15th-minute opener in Ta' Qali, and any Maltese hopes of a comeback were ended by Benjamin Kololli's strike with 20 minutes remaining.
Striker Donis Avdijaj, who plays for Dutch top-flight club Willem II, added a double and Werder Bremen midfielder Milot Rashica's 86th-minute fifth completed the rout.
Azerbaijan stayed in contention by seeing off the Faroe Islands 2-0 in Baku.
Elsewhere, Sweden kept their hopes of promotion to League A alive as Andreas Granqvist's 71st-minute penalty gave the World Cup quarter-finalists a 1-0 win in Turkey to relegate their opponents.
The Scandinavians can finish top of Group 2, despite failing to win their first two games, if they beat Russia in Stockholm on Tuesday.