Delibasic opened the scoring after 14 minutes and made it 2-0 at the break when he doubled the home side's lead on the half-hour. Elsad Zverotic added the third in the second half.
Montenegro's third straight win takes them two points clear at the top of the group having played the same number of games as England. Poland sit in third place a further three points behind, having played a game less.
Meanwhile, David Healy spared Northern Ireland's blushes with an equaliser from a free-kick deep into injury time to snatch a 1-1 draw against Azerbaijan at Windsor Park.
Rauf Aliyev had given the visitors a fifth minute lead with a stunning 25-yard strike but Michael O'Neill's men struck back for a point that is still unlikely to be good enough to salvage their World Cup dream.
The result leaves Northern Ireland in fourth place in the group with three points from four games, four points behind Israel and Portugal who are tied in second. Azerbaijan are a further point adrift.
Wednesday's World Cup European Qualifier Results
Montenegro 3-0 San Marino