Santner was dropped with three runs needed and one wicket in hand, and last man Jayden Lennox survived reviews for caught behind and lbw, before New Zealand edged past West Indies' modest total of 188 with 35 balls remaining in Bridgetown on Sunday.
The New Zealand captain hit the winning runs from the first ball of the 45th over to finish 34 not out and to spoil West Indies' hopes of achieving a series-leveling victory to pay tribute to cricket legend Garry Sobers.
"It probably shouldn't have got that close but it was nice to get over the line," Santner said.
West Indies had expressed a fervent hope to honour Sobers in his hometown of Bridgetown and at Kensington Oval, the stadium where he nurtured his career and made his name. Sobers died Friday aged 89; both teams wore black armbands and flags flew at half staff in his memory.
West Indies' hopes suffered an early setback after New Zealand won the toss and chose to bowl.
Conditions were difficult and West Indies slipped to 3-58 and 6-81 before the innings was revived by a partnership of 81 for the seventh wicket between Amir Jangoo and Gudakesh Motie.
Jangoo scored 51, his half century from 71 balls, as West Indies ground their way toward a modest total. Motie made 41.
Young pacer Matthew Fisher took 3-40 in eight overs, his first wickets for New Zealand in one-day internationals. His first wicket was that of West Indies captain Shai Hope (2) who fell to the best ball of the day, a cross-seamer which jagged back sharply from outside off.
Despite a bad start to its chase — losing two wickets with only six runs on the board — New Zealand were heading toward a comfortable win after Chapman put on 65 for the fifth wicket with Michael Bracewell. Chapman's dismissal left New Zealand at 5-142, needing only 47 runs to win with almost 25 overs in hand.
Spinner Motie and pacer Alzarri Joseph epitomised West Indies' desire not to give the game away without a fight, bowling their team to the brink of victory. Motie took 5-47 and Joseph 1-23, in 10 overs each, putting heavy pressure on New Zealand through the closing overs.
Bracewell was out for 32 to Motie's first ball after a short rain break, then Nathan Smith (8), Jacob Duffy (1) and Fisher (1) all came and went quickly.
New Zealand needed eight runs when Lennox came to the wicket at No. 11. Santner took New Zealand within one run of victory but left Lennox to face a full over from Vitel Lawes which yielded two confident appeals, both rejected under review.
Lennox survived and Santner finished the match from the first ball of the next over.
