Two goals each from Fatos Beqiraj and substitute Andrija Delibasic and one each from Luka Djordjevic and another substitute, Elsad Zverotic, sealed a comprehensive win for the visitors.
The win continued Montenegro's unbeaten start to Group H, giving them four points from their opening two games.
Djordjevic opened the scoring in the 24th minute, finishing from close range after Aldo Simoncini had parried Stevan Jovetic's shot.
Beqiraj made it two two minutes later when a low shot from inside the area and added a third seven minutes after the break with another accurate effort.
Zverotic drilled home number four from 25 yards in the 69th minute and, as Montenegro continued to look for more goals, Delibasic converted the rebound after Simoncini had kept out a Dejan Damjanovic shot.
Delibasic scored again in the 82nd minute from Filip Kasalica's left-wing cross to complete an emphatic win.