After starting their home-and-away campaign with three-straight defeats, the 'Nix dominated a lacklustre Reds side to finally earn their first bag of three points at Jubilee Stadium.
The result left Western Sydney Wanderers last on the ladder after their 4-0 thrashing from Brisbane Roar later on Friday night.
Friday night's first half between Wellington and Adelaide seemed destined to end in a goalless stalemate before Maya McCutcheon scored in the final minute of added time.
A blatant foul by Adelaide's Emily Hodgson on Japanese winger Mebae Tanaka outside the box had opened the door.
Tanaka's free kick ricocheted off numerous players before McCutcheon sent it home.
Adelaide clawed back possession in the second half but did little with their chances, failing to register a single shot on target.
Defender Mackenzie Barry had led the way for Wellington, with skipper Annalie Longo on the sidelines with a facial injury and vice-captain Rebecca Lake set to undergo foot surgery after tearing a ligament.
Longo is expected to return for the 'Nix next week after avoiding an eye socket fracture, while Lake will be out of action for six months following her surgery.
Later, the Roar surged into top spot on the ladder after Momo Hayashi's first two ALW goals laid the groundwork for victory over the Wanderers.
Signed from the NPL's Gold Coast United this season, the 29-year-old had her first goal after Wanderers captain Amy Harrison was shown a yellow card for pushing Tameka Yallop at the edge of the box.
Hayashi's free kick deflected from the wall of Wanderers defenders and past goalkeeper Sham Khamis.
After Alicia Woods struck the crossbar in her attempt to double the lead, Hayashi took matters into her own hands in first-half stoppage time.
Tamar Levin tapped the ball onto Hayashi following the Wanderers' eighth foul of the half, with the Japanese recruit poking the ball through traffic and into the right side of the goal.
Hayashi missed a handful of chances to complete her hat-trick, most notably curling yet another free kick over the goal.
But Yallop moved the Roar closer to victory by sending a long-range strike to the back of the net midway through the second half of her record-breaking 153rd game for the club.
Emily Pringle's first ALW goal sealed the Roar's equal-biggest win over Western Sydney late in the second half.
The Wanderers have now failed to score a goal in 333 minutes of regulation time.
Second-placed Melbourne City can reclaim top spot on the ladder by beating Sydney FC in Sunday's grand final rematch.
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