The Glory move to sixth and the Reds slump to last on the table after Badawiya's 39th-minute goal at the Sam Kerr Football Centre proved the difference on Sunday.
Stephen Peters' side logged back-to-back wins for the first time this season after snapping a four-game losing streak with a 1-0 win over Wellington Phoenix last round.
Adelaide United are 11th, with just one win after six games under new coach Theo Tsiounis.
The visitors dominated possession but lacked polish in attack in star forward Fiona Worts' absence.
Worts and captain Isabel Hodgson had withdrawn from the match-day squad to attend separate weddings, with the former travelling to England.
Adriana Taranto and Chelsie Dawber were left to lead the Reds' attack, but fell short of scoreboard reward in the first half.
Despite trailing on shots by 8-5 at halftime, Perth landed the first blow when Badawiya reacted the quickest to salvage the crumbs of Bronte Trew's shot.
It was American forward Badawiya's third goal for the Glory since making the move from last year's champions Central Coast.
Erin Healy tried to answer the call in the second half to keep Adelaide in the game and caused chaos across both wings.
Attacking midfielder Healy first set up Emily Hodgson in the 59th minute, but the shot was easily collected by goalkeeper Teresa Morrissey.
Healy couldn't add the finishing touches when Hodgson returned the favour seven minutes later, sending her strike too wide while fending off two Glory defenders.
The Irish international popped up again in the 72nd minute with a cross from the left wing, but Lara Gooch's header went straight into Morrissey's gloves.
Adelaide will be left lamenting their wastefulness after taking a total of 17 shots to Perth's eight.
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