West Indies had moved on to 42 without loss in their second innings, needing a further 359 to reach their victory target of 401 and achieve their first away Test win against major opposition in seven years.
Chris Gayle was 24 not out and Daren Ganga nine not out in the first match of a four-Test series.
England, a bowler light with Matthew Hoggard off the field since Saturday because of a thigh problem and without all-rounder Andrew Flintoff, who missed this match due to a recurrence of a left ankle injury, needed Stephen Harmison to find his form after a wayward first innings return of one for 117.
Andrew Strauss, England's captain in the absence of the injured Michael Vaughan, opened up Monday with Harmison and fellow Durham quick Liam Plunkett as West Indies resumed on seven without loss.
But they rarely troubled the tourists' openers.
Strauss was soon turning to left-arm spinner Monty Panesar, who'd been England's bowling star in West Indies' first innings with six for 129.
However, when Panesar was about to come on for Monday's ninth over, the umpires then halted play because of rain.
That England were able to set a stiff chase owed much to Kevin Pietersen's dashing 109 in a second innings total of 284 for eight declared.
West Indies, who'd seen England pile up an imposing 553 for five declared in their first innings, fought back gamely to avoid the follow-on but were bowled out for 437.
The tourists' performance was all the more creditable given that two days of their three-day game against Somerset, their lone warm-up fixture in England before this match, were washed out.
Panesar's haul included five lbws - the first time this had been achieved in a Test innings by a spinner and only the fifth instance in all.
England's first innings saw Matt Prior become the first England wicket-keeper to score a century on Test debut with a rapid 126 not out.
Paul Collingwood (111), Ian Bell (109 not out) and Alastair Cook (105) also reached three figures, four England batsmen scoring hundreds in the same Test innings for the first time in 69 years.
The second Test at Headingley is due to start on Friday.