Hazard sent the visitors on their way with the opening goal from the penalty spot after Lukaku had been brought down in the area by Sverrir Ingi Ingason.
Lukaku doubled Belgium's advantage just after the half-hour mark. Goalkeeper Hannes Halldorsson could only parry a Vincent Kompany header, and Lukaku was on hand to prod home from close range.
The Manchester United striker then sealed the win with just nine minutes of normal time remaining. He side-footed home Dries Mertens' cross from the right to secure all three points.
Hazard Could Be Set for Best-Ever Season
Hazard was Belgium's talisman again, as he continues the fine form he has shown since the start of the season.
He opened the scoring from the penalty spot after Lukaku had been fouled. Journalist Kristof Terreur highlighted how he is consistently producing the goods for his country:
The Chelsea star was a menace throughout, causing the Iceland defence all sorts of problems with his pace, direct running and skill on the ball.
Hazard's performance follows on from his start to the season with Chelsea. The 27-year-old has two goals and two assists in four appearances for the Blues under new manager Maurizio Sarri.
The Belgian appears to be approaching the best form of his career after a tough campaign last season under Antonio Conte at Chelsea.
Hazard frequently cut a frustrated figure, as Chelsea mounted a poor defence of their Premier League title.
The Blues ultimately finished the season in fifth, which saw them miss out on a place in the UEFA Champions League.
Conte opted to use Hazard as a false nine at times, notably in Chelsea's 1-0 defeat to Manchester City. The Belgian did not seem to enjoy the role and offered his reaction after the game, per Simon Johnson at the Evening Standard:
It's a different story this season with Sarri willing to give Hazard the freedom he yearns for. Hazard appears happy with his new manager so far, as shown by ESPN FC:
The change in approach appears to be working for Hazard, who looks unstoppable on current form and heads back to Stamford Bridge with two goals from his two games with Belgium.
Hazard was linked with a move to Real Madrid over the summer. The Spanish giants were reportedly willing to spend £200 million to bring him to the Santiago Bernabeu, per Neil Fissler and Lloyd Johnson at the Daily Express.
If he continues his fine early season form, he may do enough to convince Los Blancos to make him their next galactico signing.
Belgium's next fixture is a Nations League clash against Switzerland on Friday, October 12. Iceland play an international friendly a day earlier against France.