The former England international, who switched his allegiance to The Elephants ahead of their Nations Cup defence, came off the bench in Abu Dhabi to provide the perfect cross for Giovanni Sio who headed home a winner.
An own-goal from Wilfried Kanon had put Sweden ahead, with Yao Serge Nguessan equalising on the stroke of half-time.
24-year-old Zaha was born in Ivory Coast but has two England caps having played against Sweden in November 2012 and Scotland the following year.
As both were friendly matches, he was permitted to commit his international future to his country of birth.
The Ivorians have been preparing for the Nations Cup in the United Arab Emirates.
They will be heading to Gabon on Thursday and will play their opening Group C game on 16 January against Togo.
In other friendly internationals this weekend, Algeria were 3-1 winners over Mauritania; Burkina Faso beat Mali 2-1; Uganda defeated Slovakia 3-1; Senegal were 2-1 winners over Libya and Egypt recorded a rare victory over North African rivals Tunisia, winning 1-0.

The other contestants to have been announced so far are; Peter Andre, Carol Kirkwood, Katie Derham, Georgia May Foote, Kellie Bright, Ainsley Harriott and Jeremy Vine. More are still to be announced.
Mr O'Donnell said that he is nervous, despite his many years in show-business.
"It's really happening," he said.
The singer said he is uncertain if he is up to the standard required.
"I can put a few steps together, but can I dance to the level I need to dance? Well, that's a whole other ball game."
Earlier this year, the Kincasslagh man decided to take a short break from touring.
"I told myself that I would only consider doing something if it was both different and exciting. Well, what could be more exciting than Strictly Come Dancing? I love to dance and boy am I looking forward to getting started and being the best that I can be," he added.
Daniel O'Donnell, who has sold more than 15m albums, first rose to fame in 1983 and has had considerable success in Ireland, the UK, the US and Australia.
Strictly Come Dancing returns to BBC One for its 13th series in September 2015.
Crystal Palace winger Wilfried Zaha provided the decisive cross on his Ivory Coast debut as the African champions beat Sweden 2-1 in an Africa Cup of Nations warm-up match on Sunday.
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Irish singer Daniel O'Donnell has been confirmed as the eighth contestant on this year's Strictly Come Dancing.