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The result leaves the fourth-placed Strikers (three wins, three losses) just three points ahead of fifth-placed Melbourne Stars.
Adelaide mustered 9-146 with Alex Carey playing a lone hand, making 82 from 59 balls – only two of his teammates reached double-figures.
Perth paceman Jhye Richardson was the chief destroyer, taking 3-19.
And Englishman Roy ensured the Scorchers’ run chase was on track from the start.
He dominated a 57-run opening partnership with Liam Livingstone, who made eight in the stand.
Roy, who smashed seven fours and six, and Livingstone were dismissed in a three-ball span by Wes Agar (2-43).
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And when Perth’s Colin Munro (six) fell cheaply, the visitors wobbled momentarily at 3-80 in the 11th over.
But Josh Inglis (44 not out from 31 balls) and Mitchell Marsh (38 not out from 28 balls) calmly ensured victory with an unbroken 67-run partnership.
Marsh praised Roy’s flying start to the chase, which settled the nerves of the previously winless Scorchers.
“It’s a bit of a relief,” Marsh told Fox Sports.
“Five games in and we kept saying ‘we will get the next one boys’ and finally got one.
“The way we played tonight was outstanding, it was a full 40-over effort and now, we’re away.
“We were clinical. Jason Roy got us off to a really good start.”
Earlier, Adelaide’s Carey struck a dozen fours and a six but received scant support, with Matt Renshaw (19 from 17 balls) next-best and No.9 Danny Briggs making 10.
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The Strikers struggled for traction after losing openers Phil Salt (four) and Jake Weatherald (six) inside 15 balls.
Carey and Renshaw put on an innings-high partnership of 48 runs but Adelaide lost frequent wickets, with paceman Richardson superb and Aaron Hardie collecting 2-21 from four overs.
