The visitors, chasing an unlikely victory target of 455, were 22 for one at the close after having bowled England out for 313 at Old Trafford.
Paceman Steve Harmison took the only West Indies wicket to fall, trapping stand-in captain Darren Ganga lbw for nought.
Earlier, Alastair Cook (106) led the way in England's second innings with his sixth Test hundred.
Medium-pacer Darren Sammy was the pick of the West Indies attack, grabbing seven for 66 including three wickets in one inspirational over.
Sammy's bowling performance was the second best by a West Indian debutant.
Cook and Michael Vaughan put on 98 for the second wicket before the England captain was caught and bowled for 40 by the athletic Sammy.
Kevin Pietersen then joined forces with left-handed opener Cook to share a stand of 122 for the third wicket.
Fine-leg Corey Collymore spilled a catch when Cook was on 42 and Pietersen was also dropped on 32 and 51.
But Pietersen's luck ran out when his helmet came off his head and fell on to the wicket as he tried to hook a short ball by Dwayne Bravo.
The middle-order batsman, bidding to score a century for the third consecutive Test, looked stunned as he walked his way back to the pavilion.
The first of three streakers after tea failed to affect Cook's focus as he pulled Sammy to reach his century, becoming the ninth batsman in history to score six Test hundreds by the age of 22.
Cook finally fell when he was trapped lbw by off-spinner Chris Gayle.
Sammy's triple-wicket over came when he removed Ian Bell (2), Matt Prior first ball and Liam Plunkett for another duck.
The medium-pacer celebrated his third wicket in the over by sinking to the ground and waving his fists in the air in delight.
But West Indies joy turned to sorrow when wicketkeeper Denesh Ramdin, standing up to the stumps, was struck beneath the eye by a lifting ball from Gayle.
England are 1-0 up in the four-match series.