The victory of the world’s second-ranked team was in stark contrast to their limp defeat in their opening Euro 2016 match against Italy.
Despite dominating the opening half, it still took until the opening minutes of the second period for Belgium to take the lead when Lukaku finished a counter-attack by rifling a shot into the far corner.
Ireland had a brief positive spell but Witsel made it two for Belgium with a pinpoint header after 61 minutes, and Lukaku completed the rout with a simple finish after another counter-attack nine minutes later.
With Italy having beaten both the Belgians and Sweden to win the group, the victory puts Belgium in second place on three points with the Irish and Sweden stuck on a point apiece.
“We were under pressure before today,” Belgium’s Kevin De Bruyne, the game’s outstanding player, said. “And we came out with the right reponse.”
Coach Marc Wilmots made three changes to the Belgium line-up that struggled against Italy, and they immediately appeared more vibrant and cohesive.
Their speed and fluidity improved, with the introduction of Thomas Meunier and Yannick Carrasco giving them a menace out wide which had been missing in their opener.
De Bruyne kept his place despite a subdued showing against Italy and, vastly improved, he set the tone with a searing 13th-minute corner which Toby Alderweireld headed wide, before finding his range with a free kick.
Ireland were not without their own threat, as Meunier’s adventures down the right flank left space for Shane Long to exploit, although Martin O’Neill’s side ultimately failed to register a single shot on target during the entire 90 minutes.
Belgium began to dominate, with De Bruyne’s teasing delivery forcing a diving header from John O’Shea on 20 minutes, which inadvertently set up Eden Hazard to fire over.
Wes Hoolahan then cleared off the line as Alderweireld headed another fine De Bruyne corner goalwards.
As Irish resolve strengthened, Wilmots was again left pondering how to forge an effective attacking unit from the Golden Generation’s wealth of striking talent.
It took only three second-half minutes for an answer to emerge, as De Bruyne tore down the right before crossing for Lukaku, who opened his body and sent a curling left-foot effort into the corner of the net.
The goal seemed to release the pressure on Belgium, who celebrated furiously with Wilmots in the corner while their supporters threw flares onto the pitch.
Yet Ireland were justifiably left seething as Alderweireld’s penalty-box high foot on Long in the build-up went unpunished.
Witsel put the contest beyond the Irish 13 minutes later, arriving in the box to head the impressive Meunier’s cross beyond Randolph, whose outstretched hand could not quite divert the thumping effort wide.
In the 70th minute, Belgium added a third in a delicious move that encapsulated the invention and panache that has long been expected from this talented squad.
Meunier, again influential, dispossessed McClean and sent a long ball forward for Hazard down the right.
The attacker, outrageously lapping the linesman on the outside, raced to meet the pass before crossing for Lukaku who swept home with aplomb as Belgium secured their biggest winning scoreline at a major international tournament in 46 years.
“As a team, we had to give a response to everybody who watched the game against Italy,” Hazard said. “The way we responded was good and we really deserved this victory.”
For Ireland, though, there was nothing but disappointment as their winless run at the European Championships was extended to seven games.
“When you’re attacking you’re at your most vulnerable,” O’Shea said. “So we’ll have to work on that.”
This was an emphatic response from Belgium to their critics.
With their first clean sheet in nine matches and a dazzling second-half performance, they had finally realised their potential in a high-profile fixture, reaffirming their title credentials with clinical precision and real style.