This was England's second successive win in Group C.
Electing to bat, England made 282 for seven from 50 overs and then bundled out West Indies for 221 in 43.4 overs.
There were two half-centuries from Dan Lawrence (55) and Callum Taylor (59), besides useful contributions from George Bartlett (48) and Sam Curran (39).
In reply, West Indies lost two wickets with no runs on the board as Curram took the early wickets.
Gidron Pope (60) put on 82 runs for the third wicket with Keacy Carty (22) before Keemo Paul took the fight into the rival camp with a aggressive 65 off 58 balls.
But in the end, West Indies fell in the 44th over.
Lawrence followed his half-century with two wickets to be adjudged the player of the match, but the bowling honours went to seamer Saqib Mahmood, who claimed four for 42.
England now need a point in their last match against Zimbabwe on Sunday to finish as group leader, while the West Indies need to win both their remaining games convincingly to march into the Super League stage.
Namibia made a creditable start in Group A with a surprisingly comfortable nine-wicket rout of Scotland to keep their dream alive of making the Super League quarter-finals for the first time.
Brief scores:
Group A: Namibia beat Scotland by nine wickets
Scotland: 159 all out in 36.3 overs (Owais Shah 39, Haris Aslam 31; Michael van Lingen 3/19).
Namibia: 162 for one in 26 overs (SJ Loftie-Eaton 67 not out, Niko Davin 52, Zane Green 39 not out).
England: 282 for 7 in 50 overs (Dan Lawrence 55, Callum Taylor 59, George Bartlett 48; Gidron Pope 2/45).
West Indies: 221 all out in 43.4 overs (Gidron Pope 60, Keemo Paul 65; Saqib Mahmood 4/42, Sam Curran 2/23, Dan Lawrence 2/38).
Zimbabwe beat Fiji by seven wickets.
Fiji: 81 all out in 27.4 overs (Wesley Madhevere 5/24, Blessing Mavuta 3/13).
Zimbabwe: 84for 3 in 18.5 overs (Brendan Sly 29 not out, Jeremy Ives 23).
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