The Everton hitman struck either side of Axel Witsel’s 61st-minute header as the Belgians put their opening loss to Italy behind them and began to live up to their ranking as the second best team in the world.
Marc Wilmots’ men simply had too much for Ireland, who barely landed a blow at the Nouveau Stade de Bordeaux with Belgium dominating possession from the off and forcing them on to the back foot.
But Ireland could find neither the defensive resilience, nor a cutting edge further up the field to trouble a team packed with household names, and while the Belgians will need just a point against Sweden in their final Group E game on Wednesday to secure second spot, the Republic will need to beat Italy in Lille to stand any chance of progressing.
O’Neill had been at pains to underline the depth of individual talent available to Wilmots and play down talk of disharmony within the Irish camp, and his caution proved well-founded as his side battled simply to stay afloat during a difficult opening 45 minutes.
The Belgians dominated possession with full-backs Thomas Meunier and Jan Vertonghen joining forces with wide men Yannick Carrasco and Eden Hazard, and Kevin de Bruyne relishing the freedom given to him by Mousa Dembele.
However, Ireland managed to get themselves to the break unscathed, if largely by virtue of some last-ditch defending and some sub-standard finishing.
For all Belgium threatened repeatedly, keeper Darren Randolph had few saves of note to make in the first half, fielding one scuffed De Bruyne effort as defenders Toby Alderweireld and Meunier both missed the target when presented with opportunities.
De Bruyne’s set-piece delivery piled the pressure on Ireland and it was from his 13th-minute corner that Alderweireld glanced wide.
However, Belgium should have been ahead eight minutes later when, after John O’Shea could only head De Bruyne’s cross into his path, he blazed wastefully high and wide.
Wes Hoolahan, whose goal against Sweden almost got Ireland’s tournament off to the best possible start, came to the rescue three minutes before the break when he headed off the line after Alderweireld had connected with another De Bruyne corner.
For their part, Ireland had only one effort on goal with keeper Thibaut Courtois helping Stephen Ward’s looping 19th-minute header onto the roof of his net.
They were appealing in vain for a penalty within two minutes of the restart when striker Shane Long appeared to take a boot in the face as central defenders Thomas Vermaelen and Alderweireld attempted to prevent him from reaching Robbie Brady’s teasing free-kick, but worse was to come.
Referee Cuneyt Cakir waved play on and Belgium broke at pace with De Bruyne surging down the right before picking out Lukaku, who shifted the ball on to his left foot before drilling into the bottom corner with Randolph powerless to resist.
Ireland knew they had to throw caution to the wind in search an equaliser and went close when Brady saw a close-range shot blocked by Meunier with 59 minutes gone, but the Belgian defender helped to turn the screw two minutes later when he crossed for Witsel to power a header past Randolph and effectively seal victory.
There was no way back for the Republic with 20 minutes still remaining when substitute James McClean was robbed by Meunier. He found Hazard, who skipped away from the white shirts before handing Lukaku his second of the afternoon on a plate.