Needing a further 28 runs for victory, England lost Nasser Hussain for five to the second ball of the morning.
However left-handers Mark Butcher and Graham Thorpe guided the visitors to their target of 99 for England to retain the Wisden Trophy they won at home four years ago.
Butcher hit the winning runs to finish on 46 not out while Thorpe, top scorer with 90 in the first innings, struck three boundaries for an unbeaten 13.
England, who won the first Test in Jamaica by 10 wickets, need to avoid defeat in either of the final two Tests to seal a first series triumph in the Caribbean since 1968.
West Indies manager Ricky Skerritt immediately announced his resignation, effective from the end of June this year.
Having dismissed West Indies for 208 early on the second morning, with fast bowler Steve Harmison taking six for 61, England stayed on top for the rest of the match.
The stand of 120 between Butcher and Nasser Hussain, that spanned days two and three, set the platform for England's first innings of 319 and a lead of 111, with Thorpe top-scoring just 10 runs short of his 14th Test century.
When Ridley Jacobs, promoted up the order above captain Brian Lara in a tactical move, hit a fine 70 to help West Indies to 158 for three, it looked as if they might set England a testing target on the final day.
But Simon Jones took five for 57 to trigger another West Indies collapse as their last seven wickets fell for 51 - including Lara for eight -- leaving England with a victory target of just 99.
After rattling up 71 runs on the fourth evening, England suffered a couple of early jitters when Hussain fell for five to the third ball of the morning. Had Jacobs held on to a catch off Thorpe's second ball, the result might have been closer.
But an off-drive for four from Butcher earned England a seven-wicket victory to put them on the verge of an historic series triumph.
Scoreboard:
England first innings 319 (G.Thorpe 90, M.Butcher 61, N.Hussain 58)
West Indies second innings 209 (R.Jacobs 70; S.Jones 5-57)
England second innings (overnight 71-2)
M.Trescothick b Best 4
M.Vaughan lbw b Sanford 23
M.Butcher not out 47
N.Hussain c Jacobs b Sanford 5
G.Thorpe not out 13
Extras (b-4 lb-2 nb-1) 7
Total (for three wickets, 15 overs) 99
Fall of wickets: 1-8, 2-59, 3-71
Did not bat: A.Flintoff, C.Read, A.Giles, M.Hoggard, S.Jones, S.Harmison
Bowling: Best 4-0-27-1, Collins 4-0-26-0, Sanford 4-1-32-2, Collymore 3-1-8-0 (nb-1)
Result: England won by seven wickets and lead series 2-0.
First Test: Kingston, Jamaica - England won by 10 wickets.
Third Test: Bridgetown, Barbados - April 1-5.
Fourth Test: St. Johns, Antigua - April 10-14.
