Having waited on the fringes since round one of last season, Dos Santos made the most of her second ever appearance for the club by finding the back of the net with a brilliant header in the 72th minute on Friday.
The Sky Blues had been edging towards ascendancy, with Matildas star Cortnee Vine outsmarting goalkeeper Brianna Edwards to run into an empty goal just a minute earlier.
Under siege by defender Michaela Foster, Vine was pushed to the right and missed her shot.
The win marks their first victory after two consecutive draws and what coach Paul Temple hopes will be the start of a more consistent run of form.
Vine had been their only goal scorer in December, with two to her name before Dos Santos set the pitch alight.
Exploding to life from the opening whistle, the hosts controlled the first term and should have drawn first blood and more if it had not been for their inaccuracy.
Out of 19 total shots made in the first stanza, only seven were on target.
Vine raced out of the blocks but sent the ball too wide of the net at the seventh minute.
Forming a potent attacking partnership with Vine, star midfielder Mackenzie Hawesby announced her return with relentless attempts at goal, but was similarly dogged by a lack of precision.
The 23-year-old and three-time premiership winner rejoins the Sky Blues after making one appearance for Women's Super League club Brighton and Hove Albion.
Sydney had their best chance at opening their account when Kirsty Fenton pulled off a brilliant cutback to Aideen Keane in the box after receiving the ball on the left wing from skipper Princess Ibini.
Keane was almost certain to lob goalkeeper Brianna Edwards in the 26th minute, but she was denied on the line thanks to the quick reflexes of Foster.
Ibini took matters into her own hands just five minutes later with a brilliant individual run capped by a thundering shot outside the box that went over the goal.
Macey Fraser led the Wellington attack in the first half, but slow shots made for easy collections by goalkeeper Jada Whyman.
American striker Isabel Cox looked close to pulling one back against the hosts just two minutes after Dos Santos scored, but Whyman proved to be unconquerable.
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