Set a target of 143 at Grenada's National Cricket Stadium, Gary Ballance was 81 not out while skipper Alastair Cook was unbeaten on 59.
Earlier, West Indies had been dismissed for 307 in their second innings.
The first Test in Antigua last week ended in a draw while the third and final Test gets underway in Barbados on Friday.
Brief scores: West Indies 299 and 307; England 464 and 144 for one.