The hosts had seen their hopes of reaching Brazil dashed by defeat against England on Friday, and they could not rouse themselves.
Moldova took the lead in the 28th minute, Alexandr Antoniuc tucking home after Savo Pavicevic had blocked Vitali Bordiyan's shot.
Montenegro pulled level 11 minutes after half-time from the penalty spot after Vladimir Bozovic had been fouled by Victor Golovatenco.
And two minutes later they had a third, Eugen Sidorenco finding the top corner from 20 yards.
Artur Ionita took aim from even further out in the 73rd minute, and Antoniuc made it 5-1 in the 89th minute before Jovetic grabbed his second in injury time.