Lukaku was bundled over by Sverrir Ingi Ingason in the box for a penalty that Chelsea midfielder Hazard converted to open the scoring.
The Manchester United forward got on the scoresheet himself two minutes later with a close-range finish.
He then added a third with a deft flick nine minutes from full-time.
It was Belgium's first game in the new competition and ended a run of 13 competitive matches unbeaten at home for Iceland, who were hammered 6-0 by Switzerland away in their opening Nations League game on Saturday.
Tags:
Uefa Nacional Legue