Chasing South Africa's 300 for seven, the West Indies ended on 283 with Sammy not out on 58 from just 24 deliveries which included six towering sixes and a pair of fours.
Amla dominated an opening stand of 89 with captain Graeme Smith [ Images ] (37) then partnered Kallis as they put on 79 for the second wicket. AB de Villiers [ Images ] hammered 41 from 35 balls with three fours and a six.
Dwayne Bravo [ Images ] rallied the West Indian response with 74, including three fours and two sixes, after opener Dale Richards - who was flown in overnight from Barbados - made 51.
With the game looking lost at 200 for six in the 40th over, Sammy reignited Windies hopes with a six-filled innings which took the team within 18 runs of victory before they ran out of wickets.
Three matches remain in the series. The next is on Friday in Dominica.
G Smith b Miller 37
H Amla c Richards b Taylor 92
J Kallis c Richards b Pollard 85
A de Villiers c Taylor b Pollard 41
D Miller not out 26
A Petersen lbw b Taylor 1
R McLaren [ Images ] not out 8
Extras: (b1, lb4, w5) 10
Total: 300 for 5 (50 overs)
Fall of wickets: 1-89, 2-168, 3-239, 4-276, 5-278.
Bowling: Taylor 9-0-50-2, Rampaul 8-0-58-0, Bravo 10-0-63-0, Miller 2.5-0-19-1, Gayle 7.1-0-41-0, Sammy 5-0-25-0, Pollard 8-0-39-2.
C Gayle c McLaren b Morkel 26
D Richards b Kallis 51
R Sarwan c de Villiers b Botha 6
N Deonarine c Miller b Tsotsobe 7
D Bravo c Kallis b Steyn 74
K Pollard c Botha b Morkel 29
J Taylor b McLaren 6
D Ramdin run out (Miller) 2
D Sammy not out 58
R Rampaul run out (McLaren) 5
N Miller run out (Smith) 0
Extras: (b1, lb6, w12) 19
Total: 283 (48.1 overs)
Fall of wickets: 1-40, 2-77, 3-119, 4-182, 5-189, 6-200, 7-236, 8-236, 9-283.
Bowling: Steyn 10-0-59-1, Tsotsobe 9-1-53-1, Morkel 9.1-2-58-3, McLaren 7-1-41-0, Botha 10-0-58-1, Kallis 3-0-7-1.