After being frustrated by the Irish in the first half, Belgium broke through when Lukaku struck three minutes after the restart, atoning for his profligacy in front of goal in Monday's 2-0 loss to Italy.
Midfielder Axel Witsel headed home in the 61st minute and Lukaku got his second and Belgium's third 20 minutes from the end as Belgium came good at last, albeit against a limited Ireland team who worked hard but created little.
More than anything the win should reinvigorate Marc Wilmots' Belgium side before their last match with the Swedes and will certainly boost the confidence of Everton striker Lukaku.
Wilmots had promised to make changes in the wake of the Italy defeat and Lukaku was expected to be axed after being guilty of one vital miss in that match.
But he kept his place, as did Kevin De Bruyne, who had also been criticised and had been carrying a knock. Instead, right-back Laurent Ciman and midfield pair Marouane Fellaini and Radja Nainggolan dropped out, with Mousa Dembele, Yannick Carrasco and Thomas Meunier all coming into the side.
Ireland manager Martin O'Neill had promised a different approach from his team after what he called an "accomplished" showing in drawing 1-1 with Sweden, and it worked in the first half as Belgium struggled to create openings.
Hazard blazed a great chance over after John O'Shea headed out a De Bruyne cross into his path, while Carrasco had a goal correctly disallowed for offside.
Belgium broke quickly with Lukaku releasing De Bruyne wide on the right. The Manchester City playmaker worked the ball back into the middle for Lukaku, who took a touch before beating goalkeeper Darren Randolph with a neatly-placed shot into the bottom-left corner from 20 yards.
Meunier collected a pass from Carrasco on the right and crossed for Witsel, who stole away from James McCarthy to head in from point-blank range, with Randolph only able to help the ball on its way in.
Ireland were demoralised and Belgium picked them off on the counter to make it three with 70 minutes played.
Again Meunier was involved, robbing James McClean near his own corner flag and finding Hazard. The Chelsea star flew down that same right flank and into the middle before squaring for Lukaku, who had an easy finish in front of the massed Belgian support.
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