The former England international, who switched his allegiance to the Ivory Coast ahead of the defence of their African Nations Cup title, provided the perfect cross for Giovanni Sio to head home a 50th minute winner.
An own goal from Wilfried Kanon had Sweden ahead in the 42nd minute as he botched an attempted clearance of Nicklas Barkroth's cross but Yao Serge Nguessan equalised on the stroke of half-time.
The Ivorians have been preparing for the Nations Cup in the United Arab Emirates.
They will be heading to Gabon on Thursday and play their opening Group C game on Jan 16 against Togo.