Having lost the first match by 24 runs, Ireland won the second, rescheduled clash by five wickets to take the series into a decider.
On Sunday the visitors turned on the style to secure victory in Kingston with 31 balls to spare.
Things had started well for the West Indies as Shai Hope cracked 53 from just 39 balls at the top of the innings after Ireland had won the toss and elected to bowl.
But Hope fell to Craig Young, with the hosts losing three wickets for just four runs as the middle order failed.
Jason Holder ensured a competitive score with an impressive 44 before being run out, with the West Indies all out for 212 — Odean Smith remained unbeaten on 20 from 10 balls.
Ireland could not have made a more contrasting start as William Porterfield was out off the first ball of the reply, caught by Akeal Hosein off the bowling of Alzarri Joseph.
Captain Paul Sterling (44) put on 73 runs with McBrine before he was trapped lbw by Hosein — but then McBrine and Tector went to work, the pair shining once more to add 79 for the third wicket.
McBrine (59) and Tector (52) would eventually fall and there was a wobble from the tourists with no one else scoring more than 11 runs but they still had enough to get over the line as Young found the boundary to secure the victory and the series.
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