The left-hander unsurprisingly collected the Player of the Match honour for his efforts.
“I don’t think it’s sunk in yet. It will take some time for me to get my head around what happened in this Test match,” Conway said.
“But I’m really glad we got the win.”
The victory sees the Black Caps surpass South Africa and move into second place on the World Test Championship standings, with trans-Tasman rivals Australia the only side in front of them. The Black Caps next take on England in a three-match World Test Championship series in the middle of next year.
The West Indies remain in ninth place on the standings, with their next contest coming at home in the middle of next year against Sri Lanka and Pakistan.