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.
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.