Eduardo, out since last February following a horrific leg injury, set up a close-range finish for Niko Kranjcar, another long-term casualty making a successful international return.
"It was easy to score after Eduardo's perfect assist, we all knew he would be back with a roar. We all believed in him and we are all aware how much stronger we are with him," Kranjcar told reporters.
"The win will give us a new impetus ahead of testing World Cup qualifiers," the Portsmouth midfielder added.
He was absent from the finals in Austria and Switzerland after suffering a fractured fibula and an open dislocated ankle during last season's Premier League match at Birmingham.
"I am delighted to have Eduardo back and his return is an enormous bonus for us," said Bilic.
"His ball control, the ability to hold it and wait for support has been sorely missed and it makes all the difference when we play top-level opposition."
