The pair stuck 93 run partnership for the first wicket before Shannon Gabriel provided the breakthrough in the form of Bairstow’s wicket.
Woakes and Root then stitched together a 104 run partnership and brought them closer to victory. Just when they were striking distance of a win, Woakes was caught in long on.
In the meantime Root got to his 2nd century of the world cup and with Stokes in company at the other end won the match with 8 wickets in hand.
Earlier, Mark Wood and Jofra Archer picked up three wickets apiece to end West Indies innings at 212 all out, with over five overs left.
For England the other notable contribution came from Joe Root who struck twice to bring England back in the game.