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.
The result put Belgium in prime position to qualify for the last 16 from Group E and also confirmed Italy as group winners, a day after the Azzurri secured their progress to the next round with a 1-0 victory over Sweden.
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.
Belgium utterly dominated possession in the first 45 minutes against an Irish side that set out to frustrate their more illustrious opponents, and captain Eden Hazard was the one pulling the strings.
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.
Toby Alderweireld also saw his header from a De Bruyne corner cleared off the line as the first period ended goalless, but Wilmots opted against making any changes at the interval and he was rewarded for his patience as the opener came soon after the restart.