Liverpool midfielder Wijnaldum, who scored in his country's friendly defeat to Greece last week, started in midfield for the Dutch before being taken off with 24 minutes remaining.
Marcus Berg put Sweden ahead shortly before half-time at the Friends Arena in Solna, but the visitors fought back claim a point thanks to Wesley Sneijder's equaliser midway through the second half.
Elsewhere, Reds defender Ragnar Klavan played the full 90 minutes as Estonia lost 5-0 to Bosnia-Herzegovina, while Divock Origi and Simon Mignolet were both unused substitutes in Belgium's 3-0 victory in Cyprus.