With scores tied at 118 after 20 overs, Chris Barnwell swatted the first ball of the one-over eliminator from seamer Kevon Cooper over mid-wicket, to help Amazon Warriors gather 11 runs.
With Red Steel requiring 12 to win, Narine beat left-hander Nicholas Pooran outside the off-stump with the first four deliveries before having him caught at long off by Martin Guptil off the fifth ball to seal the game.
Ross Taylor also swung and missed at the final delivery as Red Steel failed to score a single run, giving Amazon Warriors their second win of the tournament following their two-wicket win over Antigua Hawksbills in the tournament opener in Grenada last weekend.
The maiden was the first-ever in a Super Over in Twenty20s.
Red Steel were left with only themselves to blame as they allowed Amazon Warriors back into the match with some sloppy fielding in the last two overs.
Defending a modest 118, the Trinidad and Tobago-based Red Steel bowled and fielded superbly to restrict Amazon Warriors to 91 for six after 17 overs, leaving the hosts with 28 runs to get from 18 deliveries.