The Phoenix were without lively midfielder Isaka Cernak for the game due to a hip flexor complaint, while Jeremy Brockie returned to the fold after missing last week's loss to Brisbane through suspension.
Brockie's return caused a shuffle in formation as Louis Fenton dropped back in to the midfield and he was joined there by Vince Lia who switched from right back after Leo Bertos also returned to the field.
Adelaide opened the scoring in the 20th minute when a delightful cross from Iain Ramsay found Tomi Juric who slammed home a powerful left foot shot on the half volley that gave Phoenix goalkeeper Glen Moss no chance.
Wellington had men in the box on defence but they didn't stick close enough to Juric and neither Andrew Durante or Tony Lochhead attacked the ball, which allowed the Adelaide striker to pounce.
The home side found their way in to the game just over 10 minutes later when Jeremy Brockie was gifted a tap-in from close range after the energetic Gameiro dispossessed Galekovic.
Brockie had made a meal of a golden scoring opportunity only moments before but made no mistake when the ball fell fortuitously in to his path after Gameiro's good work.
Before the home side even had time to catch their breath, Adelaide restored their advantage though when a thunderbolt shot from midfielder Marcelo Carrusca rifled in to the top corner of Moss' net.
The start of the second half produced a notable flat patch as Adelaide seemed content to sit on their lead while the Phoenix lacked continuity in attack as their passes failed to find their mark.
Phoenix coach Ricki Herbert waited until the 75th minute to make use of his bench when former Belgian international Huysegems was given his boarding pass to replace Vince Lia.
Considering the Phoenix had three attacking-minded players sitting on the pine it seemed a long time to wait before making use of his substitutes, particularly when they were down a goal for so long.
Huysegems provided the midas touch though when he assisted on Gameiro's strike and youngster Tyler Boyd was introduced to the game shortly after.
Boyd ran at the defence as he always does but failed to deliver the killer punch as the Phoenix couldn't find a way to take all three points.
The Phoenix host Newcastle United at Westpac Stadium on Wednesday night as they look to keep in touch with the A-League's top six.
Wellington Phoenix 2 (Jeremy Brockie 31, Corey Gameiro 80) Adelaide United 2 (Tomi Juric 20, Marcelo Carrusca 33) HT: 1-2
