Thailand chose to bat first on their global debut but struggled to score heavily at the WACA, leaving teenage keeper-batter Nannapat Khoncharoenkai to step up and anchor the innings with 33 from 48 balls.
Captain Taylor held their Group B opponents to 78 for nine with her three wickets, but Thailand’s fielding strength came to the fore with Lee-Ann Kirby, Hayley Matthews and Deandra Dottin all departing before the seventh over to spark thoughts of an upset.
But Taylor and Shemaine Campbelle stayed firm and their unbeaten fourth-wicket partnership of 53 sealed the win.
Having restricted the debutants to 12 for two within four overs, Henry continued for a third successive over and Khoncharoenkai soon found her groove when she pulled a full toss to the boundary.
It was an impressive yet calm performance from the 19-year-old who stabilised the innings from the third wicket, but her 35-run partnership with Naruemol Chaiwai (13) came to an end after seven overs when Aaliyah Alleyne caught the latter at mid-off off Anisa Mohammed.
Matthews took her first scalp when she had Chanida Sutthiruang caught and bowled for three while Taylor dismissed opposite number Sornnarin Tippoch for just 1.
The wickets kept rapidly fell around Khoncharoenkai with Taylor bagging a second when Kirby dived and snaffled Onnicha Kamchomphu - in at seven - for a duck.
With two overs remaining, Khoncharoenkai tried to up the tally and hit an Afy Fletcher delivery over the top but Kirby - playing in her international in 12 years - produced another impressive catch to her right to dismiss Thailand’s batting rock.
Chasing 79, West Indies’ were dealt an early blow as Kirby’s international comeback ended prematurely, Chaiwai producing the play of the day with a quick pick-up and direct hit to claim her country’s first Women’s T20 World Cup wicket.
That moment was a spark for Thailand, Soraya Lateh sneaking a second wicket when bowling Matthews, who played across the line, for 16 for her first international victim.
It got even better for Tippoch’s side as Dottin was run out by Suleeporn Laomi to leave West Indies on 27 for three.
But Taylor (26 not out) brought West Indies up to 50 with three boundaries and Campbelle (25 not out) swept three of her own to steer her country to their first WT20I victory in nine games and an opening success in Group B.
Scores in brief
West Indies beat Thailand by seven wickets, WACA Ground, Perth
Thailand 78-9, 20 overs (Nannapat Khoncharoenkai 33; Stafanie Taylor 3-13)
West Indies 80/3, 16.4 overs (Stafanie Taylor 26 not out, Shemaine Campbell 25 not out; Soraya Lateh 1-21)