West Indies made 241 for nine and then bowled Pakistan out for 187. It marked a superb return to form after they were crushed by India by nine wickets having been skittled for 85 in their final warm-up game on Friday.
Batting at number eight, man-of-the-match Smith's cameo of 32 from 15 balls pushed his side to a competitive total and then his medium-pace bowling turned the game in West Indies' direction.
He claimed the vital wickets of Mohammad Yousuf and Pakistan skipper Inzamam-ul-Haq in a return of three for 36.
It was an impressive performance from the Caribbean side with major batting contributions from Marlon Samuels (63), Ramnaresh Sarwan (49) and captain Brian Lara making 37. Later seamer Dwayne Bravo took three for 42.
The win gives West Indies pole position in the group ahead of their games against Zimbabwe and Ireland and two points to take into the Super Eights stage, presuming both they and Pakistan qualify.
Despite the early loss of openers Chris Gayle and Shivnarine Chanderpaul, West Indies took a grip on the game thanks to an impressive demonstration of strokeplay from Samuels who reached his fifty off 56 balls.
He reached his half-century with a thumping straight six off Shoaib Malik.
The hosts, who have shown a tendency towards middle-order slumps, could easily have lost their way following the dismissals of Samuels and Lara -- both victims of part-time off-spinner Mohammed Hafeez.
But Smith, who hit three fours and two sixes in his late show, helped West Indies to pile on 58 runs in the last five overs and set a challenging total for Pakistan to chase.
The West Indies pace attack inflicted early damage with Daren Powell claiming openers Imran Nazir and Hafeez and Jerome Taylor dismissed Younis Khan as Pakistan stumbled to 39 for three.
But then Inzamam and Yousuf dug in with a patient partnership, keeping their cool despite being tied down by some accurate bowling, particularly from the consistent line and length of Corey Collymore.
Smith broke the partnership having Yousuf caught behind for 37 as he edged an attempted cut shot to leave Pakistan 99 for four and then he turned the game when he trapped Inzamam leg before for 36.
With Smith's next ball, Kamran Akmal was sent on his way, caught brilliantly at point by a diving Dwayne Bravo.
Bravo then dealt with the lower order himself with the wickets of Rana Naved-ul-Hasan, Rao Iftikhar and Umar Gul.
With wickets running out and the run-rate rising, it needed some individual brilliance for Pakistan to turn the game around and Shoaib Malik made a lone effort with an aggressive innings of 62 from just 54 balls before he was caught at long off.