The home side seemed devoid of ideas and it appeared it was only a matter of time before Real took advantage and they eventually did so in the 19th minute.
A corner fell to Roberto Carlos who blasted a left foot drive towards goal, Ilic and Raul Gonzalez went for the ball, which deflected in, although the Real striker was credited with the strike.
Versatile star Steve McManaman struck ten minutes from the break to make it 2-0 as he latched onto Michel Salgado's shot to fire home from close range.
Raul Gonzalez could have made the game safe but screwed his shot horribly wide when put clear by Albert Celades as the Belgians failed to deal with the irresistible attacking force that Real can be.
In a talking point for Tuesday evening, Anderlecht's Aruna Dindane was only booked for a dive in the area, whereas Mallorca's Samuel Eto'o was dismissed for a similar offence.
Anderlecht were more purposeful in the second half but failed to capitalise on any of their chances, with Ivica Mornar especially guilty in front of goal.
The result sees Real Madrid qualify for the second phase, with 12 points from four games and with Roma on seven, Anderlecht need to win both their next two matches and hope the Italian side loses both if they are to progress.
Meanwhile, Roma scraped past a determined Lokomotiv Moscow 1-0 in the early game on Tuesday evening, thanks to a 77th minute own goal from Igor Cherevtchenko.
It was Lokomotiv that took the initiative and they went close without truly threatening the Italians, who eventually took control of the game as the first half wore on.
Indeed Gabriel Batistuta could have put Roma a goal to the good with a couple of minutes left when he was put through on goal by Francesco Totti, only for the Argentinian to mis-control the ball and lose the chance.
The second half was more of the same, with much effort expended by both sides but little in the way of clear cut opportunities.
Eventually the only goal of the game came with a fair degree of luck involved, as Gianni Guigou's cross came through to Cafu and the Brazilian's strike on goal cannoned off Cherevtchenko and into the home net, leaving keeper Ruslan Nigmatullin without a hope.
Striker Dmitri Loskov just failed to equalise in injury time, as Lokomotiv launched a furious assault in the final moments, but Roma had done just about enough to earn the three points.
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