Nicol top-scored with 59 off 69 balls while McCullum boosted the lower order with 50 off 70 deliveries at Warner Park.
Paceman Andre Russell took 4-57 while spinner Sunil Narine claimed 2-28 off 10 overs.
West Indies, after winning the toss, made an early breakthrough when Russell has Martin Guptill lbw for 11 after playing across the line, making the score 24-1.
Nicol then put on 47 with Daniel Flynn (28), who chased a wide delivery from Dwayne Bravo and edged to wicketkeeper Denesh Ramdin.
The innings dipped badly after that.
Kane Williamson (9) was bowled by Narine, while Darren Sammy and Marlon Samuels also claimed key wickets.