Roberto Martinez’s side needed only to avoid defeat to prevent Denmark from finishing top of group A2 and they started strongly in Leuven, Youri Tielemans putting them ahead after only three minutes.
Jonas Wind levelled in a first half in which the visitors were the more threatening side, but when Kasper Schmeichel could not quite do enough to deny Lukaku 57 minutes in, the contest was effectively settled.
Lukaku nodded in his second and Belgium’s third 12 minutes later to make certain of the victory and reach 57 goals for his country, including six in his past four appearances.
A late aberration from Courtois gifted Denmark a second but Kevin De Bruyne struck an immediate reply to quash any fear of a late comeback.
Tielemans fired Belgium ahead against England and did so again here from a similar distance, his left-foot shot from the edge of the area bobbling beyond Schmeichel and into the bottom-right corner
Denmark equalised 14 minutes later, Wind heading a loose ball beyond Courtois after Martin Braithwaite’s shot had been blocked.
Braithwaite had a great chance to make it 2-1 but was denied by a sprawling Courtois, and Lukaku nearly glanced Belgium back in front from De Bruyne’s cross.
Lukaku had cut an isolated figure but took the next chance that came his way in the second half. A quick free-kick allowed De Bruyne to feed the striker, whose shot struck the onrushing Schmeichel but looped up and over the line, with the covering Andreas Christensen only able to hook the ball high into the net
The Inter striker planted a firm header past Schmeichel from six yards out after a fine cross from Thorgan Hazard to make it 3-1, before Courtois allowed Nacer Chadli’s pass to roll beneath his foot and into the net to leave Martinez looking thunderstruck on the touchline.
De Bruyne soon calmed any nerves, though, side-footing into the net after Thomas Foket’s cross had bobbled across the Denmark box.
What does it mean? Belgium ease into Finals
The result means Belgium finish top of Group A2 with 15 points, five above Denmark and England, and it secures their place at the Finals next year.
Denmark may feel frustrated to have failed to capitalise on a sluggish display by Martinez’s men, particularly in the first half, but their performance here augurs well for the meeting between these two in the Euro 2020 group stage.
Lukaku lethal when it counts
Lukaku only attempted 21 passes, 11 fewer than goalkeeper Courtois, and often seemed detached from the action in a first half in which Denmark posed the bigger threat.
However, when his two opportunities came, he did not falter – even if Schmeichel was unlucky not to keep out his first
Sliding doors for Braithwaite
By contrast, Braithwaite could not convert his best opening when the scores were level, as Denmark failed to make the most of a good first 45 minutes.
The Barcelona man did not manage another shot until the 80th minute, by which time their fate was all but sealed.
These teams are finished for 2020 and have no fixtures set in stone before the Euros begin next June. They will face one another then, too, in a Group B game in Copenhagen on June 17.