The West Indies were mauled by nine wickets by England in their last warm-up but looked on course for a comfortable afternoon against the Scots when they piled-up 313-9 in 50 overs.
Despite losing Chris Gayle and Marlon Samuels for one run between them, the Caribbean side then saw Denesh Ramdin (88) and Lendl Simmons
Scotland opener Kyle Coetzee smashed 96 with 14 fours with Richie Berrington adding a crucial 44-ball 66.
But with a famous win in sight, Berrington was run out in the 49th over with Scotland losing two more wickets in the next six balls, as seamer Kemar Roach coolly defended a last-over target of 12 runs.
Despite the defeat, Scotland can take heart from their preparations having crushed Ireland by 179 runs in their first game.
West Indies will play Ireland in Nelson on Sunday in their World Cup opener while the Scots take on New Zealand in Dunedin the following day.
In Thursday's other warm-up, Ireland repeated their 2011 win over Bangladesh with a comfortable four-wicket victory.
Bangladesh were dismissed for a paltry 189 in 48.2 overs before Ireland reached 190-6 with 19 balls to spare.
Soumya Sarkar top-scored for Bangladesh with 45 off 51 balls with seamers John Mooney and South African-born Max Sorensen sharing six wickets.
Andy Balbirnie top-scored for Ireland with an undefeated 63.
While Ireland go on to face the unpredictable West Indies in their tournament opener, Bangladesh start against Afghanistan in Canberra on February 18.