Though Archer had captain Shai Hope caught in the first over and fellow opener Brandon King slashed Curran to deep point in the second, West Indies were always dangerous given their stacked batting line-up.
England continued to take regular wickets but only Adil Rashid, who claimed 2-16, managed to stop the scoring.
Whereas Chase took 2-29 after being brought into the XI, England’s part-time off-spinner Will Jacks was hit for 32 in two overs – Brook’s decision to give him one over in the powerplay costing 19 runs.
Archer, who also struggled against Nepal on Sunday, was wayward with his lines.
Rutherford had his moments. The first chance offered was a leading edge that flew to deep third, with Rashid unable to take the catch or flick the ball back inside the rope.
That was a tough chance but Rashid would be disappointed not to take a chance off his own bowling when Rutherford skied a slog sweep in the 18th over.
The left-hander added another 18 runs from seven balls after that miss while Holder hit four sixes, three of which came in the 18th over bowled by Curran.
With dew not playing a part in making the ball harder to grip for the West Indies bowlers, it proved too much for England when the ball turned.