After trailing on first innings, Red Force hit back strongly to bundle out the hosts for 130 in their second innings, and set themselves an uncomplicated victory target of 203 at Warner Park.
At the close, they had reached 95 for two, and were requiring a further 108 to win the contest.
Yannick Ottley was unbeaten on 40 at the close and was partnered by Jason Mohammed on 17.
The Leewards were right in it when they claimed openers Lendl Simmons (13) and Imran Khan (21) cheaply but Ottley and Mohammed steadied the innings in an unbroken 53-run, third wicket stand.
Ottley, a 23-year-old right-hander, has hit four fours and a six off 199 balls.
Earlier, leg-spinner Imran Khan snatched six for 13 as the Leewards, resuming on 17 without loss, were sent crashing for a modest total.
They were 62 without loss but collapsed to lose ten wickets for 68 runs in a nightmare period on either side of lunch. They lost four wickets in the morning to be 109 for four at the break and the remaining six wickets then tumbled after lunch for the addition of only 21 runs.
Opener Austin Richards top-scored with 42 off 61 deliveries while Jahmar Hamilton contributed 31.
It was Hamilton who tried to rally the innings in a knock that came from 67 balls in 76 minutes, with four fours. He put on 34 for the fifth wicket with captain Devon Thomas who scored 19.
The pair had pushed Leewards up to 121 for four but once Thomas was caught at mid-wicket by captain Rayad Emrit off fast bowler Shannon Gabriel, the last six wickets perished for nine runs.
Seamer Émrit took two for 13.