The Black Knights lost defensive stalwart Sakai to injury early on Saturday, but Louis Verstraete stood tall to score the 79th-minute match-winner at Go Media Stadium.
Reds youngster Luka Jovanovic had levelled the scores in the 45th minute, after Sam Cosgrove put the hosts ahead in the 26th minute.
Last year's premiers, Auckland remain undefeated to start the season after two wins and one draw ahead of next Saturday's derby against Wellington Phoenix at Sky Stadium.
Corica doesn't yet know the extent of Sakai's injury, but isn't expecting the defender to be fit and firing within a week.
Sakai had hurt his left hamstring in the 12th minute while chasing for the ball in Adelaide's box.
"He won't be ready for next week, 100 per cent," Corica said.
"And then we got the international week after that - depending, maybe after that, he might be fine."
Meanwhile, the ninth-placed Reds (1-0-2) are left searching for their second win under new coach Airton Andrioli after suffering two straight defeats.
Adelaide had lost 2-1 away to Macarthur FC on Monday.
"Obviously, I (also) said this last week - disappointed with the result," Andrioli said.
"We controlled the second half. They didn't have many chances, and in one moment of lapse of concentration, we conceded the goal, and we lost the game."
Callan Elliot replaced Sakai before Cosgrove finally lived up to the hype after beating Ethan Alagich to find the opener with a header.
The former Plymouth and Aberdeen striker was touted as Auckland's solution in attack after arriving in the off-season from League One outfit Barnsley.
A raucous home crowd was then silenced in the 45th minute when Reds youngster Jovanovic ousted three defenders to draw level with Auckland.
Jovanic continued to cause trouble after halftime, combining with Jonny Yull to pepper at goal.
Dominating possession, the Reds looked poised to take the lead after Auckland midfielder Verstraete gave away a free kick for fouling opposition captain Craig Goodwin in the 77th minute.
Goodwin delivered a class kick into the box, but it was Elliot who connected with the ball first.
A lapse in Adelaide's defence allowed Auckland back into the game, with Ryan White giving away possession to Francis De Vries.
Guillermo May superbly played the Reds defence for time and set up Jesse Randall, whose shot went thundering into the post.
A quick-thinking Verstraete found redemption by burying the ball home for the lead.
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