Vicento side-footed the ball past Adrian Clifton in the 87th minute to give Curacao a 4-3 aggregate victory, seconds after Bradley Woods-Garness had seemingly forced the first round clash into extra-time.
Former Netherlands assistant coach Kluivert oversaw Curacao's 2-1 win last week and he had the Midas touch again as the Caribbean nation clinched a second round tie with Cuba.
Curacao made a dream start away from home after Darryl Lachman's strike deflected into the net just three minutes prior to half-time.
Montserrat refused to surrender, though, as Jamal Willer restored parity in the 65th minute.
It got better for Montserrat nine minutes from time, when Woods-Garness put the home side ahead and levelled the tie on aggregate via a low shot that rolled into the bottom corner of the net.
But amid all of the celebrations, with the tie seemingly destined for extra time, Curacao went up the other end and netted the winner thanks to Vicento.
Curacao will play Cuba over two legs - on June 8 and 16 - for a spot in the third round.
