West Indies thrash England to reach Women's T20 World Cup semis
Joseph smashed 52 for her first T20 international half-century and skipper Matthews hit a 38-ball 50 as West Indies overhauled England's 141-7 with 12 balls to spare.
South Africa also made it to the last four from Group B while England were eliminated from the competition.
"Incredibly proud of the group. Up against the odds tonight but to put up a performance like that with the bat, with Joseph scoring her first T20I fifty - what a time to do that," said Matthews.
"We have been chasing (before in this tournament) and we back ourselves to knock off whatever runs are put on the board."
Matthews launched the West Indies chase with aplomb, hitting a six and two boundaries in the first over by Lauren Bell.
Joseph too joined the party, smashing left-arm spinner Sophie Ecclestone for two fours in a row as West Indies raced to 55-0 in five overs.
Matthews picked Charlie Dean for some special treatment, dispatching the ball over the square leg fence for three boundaries in the sixth over.
England were sloppy in the field, dropping as many as five regulation catches.
Joseph, named player of the match, was dismissed in the 13th over after hitting two sixes and six fours in her 38-ball innings.
Matthews also departed soon after but Deandra Dottin made 27 to give West Indies their first win against England in 14 matches and the first away from home in 10 years.
"Credit to them, they came at us hard, played the conditions well and put us under the pump. Tough to take but credit to Hayley and her team," said England skipper Heather Knight.
"We bowled too short and they played it well."
Put in to bat, England lost Danni Wyatt-Hodge (16) early with the opener being caught brilliantly just inches off the ground by Dottin (1-16) off Matthews (2-35).
Dottin was in the thick of action soon again when she ran out Alice Capsey for one with a sharp one-handed throw to wicketkeeper Shemaine Campbelle.
England suffered another blow as opener Maia Bouchier (14) was caught off leg-spinner Afy Fletcher (3-21) at extra cover, reducing the side to 34-3 by the seventh over.
Knight and Nat Sciver-Brunt (57) helped rebuild the innings, sharing 46 runs for the fourth wicket.
After Knight retired hurt on 21 with a calf strain, Fletcher removed Amy Jones (7) and Charlie Dean (5) in successive overs.
Sciver-Brunt was the most impressive among the England batters, hitting five fours in her unbeaten 50-ball knock.