JOIN USChasing 219 for victory, the Pakistanis were dismissed for 178 in their second innings about 50 minutes after lunch on the fourth day yesterday at the Guyana National Stadium.
Sammy finished with the impressive figures of five for 29 from 17 overs that helped him to earn the man-of-the-match award, and Rampaul supported with four for 48 from 21 overs.
Fittingly, the embattled Sammy brought the match to a climax when he bowled Pakistan bowling hero Saeed Ajmal for three.
The victory gave West Indies a 1-0 lead in the two-match series, which concludes with the second Test, starting on Friday at Warner Park in St. Kitts.
It was also the West Indies' first Test victory since February 2009, when they humbled England by an innings and 23 runs at Sabina Park in Jamaica.
"This is all about West Indies cricket," said Sammy. "We as a team needed this performance, this victory, and I can't stop commending the effort of the guys - every single person that batted on such a difficult pitch.
"It was a total team effort, and it was good to come out on the right side of the result for a change."
Sammy had been under fire from a demanding West Indies public, following a string of weak personal performances in the lead-up to the Test, but felt he had answered the critics as he celebrated his first Test victory since being put in charge last November.
"Once I step on to the field wearing that West Indies cap, I give my heart and soul," he said.
"I know things have not been going too well for me lately, but I still had the self-belief to go out there and do well - and so did my teammates."
The result also meant that Pakistan will have to wait for another trip to earn their first Test series victory in the Caribbean.
"To lose a Test match is never an easy thing," said Pakistan captain Misbah-ul-Haq, whose 52 was the top score in his side's second innings.
"But they played better cricket than us. They bowled really disciplined throughout the match, and most of the time, they got us out with good bowling."
Misbah added: "I think it was a bit of everything that went wrong for us, but our fielding especially. We dropped way too many catches.
"We gave away too many runs, especially runs scored by the tail. They had good partnerships towards the end of each innings, particularly in the second innings, and that was really crucial.
"It was also disappointing from the batting point of view, but this is how it goes sometimes."
Pakistan's bid for victory hit a problems in the final half-hour before lunch, when Sammy removed Misbah and Mohammad Salman - both lbw - in the space of three balls to leave the visitors on 153 for six at the interval.
But the result did not appear to be a formality until Sammy trapped Umar Akmal plumb lbw for 47, as Pakistan lost their last four wickets for 18 runs in the space of 31 deliveries after lunch.
Akmal's dismissal established a new record for the most lbw decisions ever in a Test of 20, erasing the previous mark of 17 between the two sides 18 years ago at Queen's Park Oval in Trinidad.
Scoreboard
West Indies 1st Innings 226
Pakistan 1st Innings 160
West Indies 2nd Innings 152
Pakistan 2nd Innings (overnight 80-3)
Mohammad Hafeez lbw b Roach 2
Taufeeq Umar lbw b Rampaul 0
Azhar Ali c Baugh b Rampaul 0
Asad Shafiq b Rampaul 42
Misbah-ul-Haq lbw b Sammy 52
Umar Akmal lbw b Sammy 47
Mohammad Salman lbw b Sammy 0
Abdur Rehman c Smith b Rampaul 6
Umar Gul lbw b Sammy 1
Wahab Riaz not out 11
Saeed Ajmal b Sammy 3
Extras (B-2, LB-11, NB-1) 14
Total (all out, 73 overs) 178
Fall of wickets: 1-2, 2-2, 3-2, 4-83, 5-135, 6-135, 7-160, 8-163, 9-166.
Bowling: Roach 13-1-30-1; Rampaul 21-6-48-4; Bishoo 21-5-56-0 (nb1); Sammy 17-7-29-5; Nash 1-0-2-0.