Matthews (66) and captain Taylor (59) added 120 for their opening stand as West Indies chased down a 148-run target with three balls to spare for their first win against the Southern Stars in nine attempts in World Twenty20.
Deandra Dottin, who took two wickets for 33, remained unbeaten on 18 to see West Indies through and spark wild celebrations among her team mates who were joined by several members of the men's side in a celebratory dance.
"We didn't get the start we wanted. In the first three overs we only scored three runs but it was good to keep wickets in hand," Taylor, who was named player of the tournament, told reporters.
"We just said: 'We could do this, just stay here and bat through'.
"I don't think it's quite sunk in as yet. We have a good feeling right now but I think when it really hits us that's when we will know."
Australia's Elyse Villani and captain Meg Lanning had both hit 52 and added 77 for the second wicket to take their side to 148 for five after they won the toss and opted to bat.
Dottin gave away just one run in the final over which according to Lanning was a crucial moment in the match.
"It was certainly a pivotal moment I guess," Lanning said. "I think we needed 160-plus on that wicket and we certainly set ourselves up to get to that mark.
"We just probably slowed a little bit towards the end including that final over. That probably gave the West Indies a little bit of momentum heading into their batting innings."
(Editing by Clare Fallon)
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