Bravo and Ramdeen staged a 65 run fourth wicket stand to swing the homeside back on course after slumping to 75 for four, chasing a winning target of 141 set by the Leewards.
Narine grabbed four wickets for 17 runs and Rampaul four for 20 to bowl out the Leewards for 140 after they had won the toss and elected to bat.
Trinidad, desperate for their first victory since losing by 28 runs to Barbados in their opening game, suffered an early setback, losing opener Adrian Barath in the first over.
Lendl Simmons attempted to steady the slide scoring 25 while three wickets fell before 100 runs came up as Leewards tried to pile on the pressure.
But the Trinidadians recovered when Bravo hit three sixes and four fours in a top score of 42 from 37 balls, Ramdeen was unbeaten on 22 while Dwayne’s brother Darren contributed the same score.
Gavin Tonge topped the Leewards bowling with three for 38 as his side crumbled to their second straight loss.
Earlier, Rampaul removed the openers and Narine, who was named man-of-the-match, carved through the middle order severely restricting the Leewards run flow.
The visitors were in trouble at 46 for four before a 67 run partnership for the 5th wicket between Devon Thomas and Jahmar Hamilton added some respectability to the total.
Thomas scored two sixes in a top score of 42 while Hamilton chipped in with 39.
Leeward Islands Innings: 140 All Out (43.2 Overs). Devon Thomas 42, Jahmar Hamilton 39, Montcin Hodge 15, Rahkeem Cornwall 14; Sunil Narine 9.2-3-1-17-4, Ravi Rampaul 9-3-20-4, Rayad Emrit 7-0-19-1, Yannick Ottley 6-0-30-1.
Trinidad & Tobago Innings: 144/5 (27.1 Overs). Dwayne Bravo 42, Lendl Simmons 25, Denesh Ramdin 22, Darren Bravo 22; Gavin Tonge 8-2-38-3, Justin Athanaze 6-1-30-2, Anthony Martin 5-0-22-0, Quinton Boatswain 6.1-1-35-0.
K Powell c Emrit b Rampaul 8
M Hodge c Simmons b Rampaul 15
M Richards LBW Narine 10
S Joseph c Simmons b Emrit 4
D Thomas c Simmons b Ottley 42
J Hamilton LBW Narine 39
R Cornwall LBW Narine 14
J Athanaze c Dwayne Bravo b Narine 0
G Tonge c Darren Bravo b Rampaul 4
A Martin b Rampaul 0
Q Boatswain not out 0
Total: 140 All Out (43.2 Overs)
Extras: (4WD) 4
Fall of Wickets: 1-20, 2-30, 3-35, 4-46, 5-113, 6-130, 7-130, 8-139, 9-140, 10-140.
Trinidad & Tobago Bowling: DJ Bravo 4-0-19-0, R Rampaul 9-3-20-4, R Emrit 7-0-19-1, S Narine 9.2-3-17-4, I Khan 5-0-24-0, L Simmons 3-0-11-0, Y Ottley 6-0-30-1.
Trinidad & Tobago (Target; 141)
A Barath c Thomas b Tonge 0
E Lewis LBW Tonge 11
L Simmons c Richards b Athanaze 25
Darren Bravo c Cornwall b Athanaze 22
Dwayne Bravo c Thomas b Tonge 42
D Ramdin not out 22
Y Ottley not out 5
Total: 144/4 (27.1 Overs)
Extras: (15WD, 2LB) 17
Did not Bat: I Khan, R Emrit, R Rampaul, S Narine
Fall of Wickets: 1-0, 2-25, 3-65, 4-74, 5-139
Leeward Islands Bowling: G Tonge 8-2-38-3, Q Boatswain 6.1-1-35-0, A Martin 5-0-22-0, J Athanaze 6-1-30-2, R Cornwall 2-0-17-0.
Result: Trinidad & Tobago won by 5 wickets
Man of the Match: Sunil Narine (Trinidad & Tobago)
Umpires: Lennox Abraham, Leslie Reifer
4th Official: Nigel Duguid
Match Referee: Hayden Bruce