The ninth minute saw another yellow card for Egypt, Ahmed Fathi taking out Carrasco, while four minutes later, Mohamed Elneny's half-volley struck Laurent Ciman, leading to half-hearted penalty calls.
Belgium were soon able to find their stride and took the lead on 26 minutes, Lukaku making the most of Essam Elhadary's weak palm into the six-yard box to finish off on the rebound.
The Red Devils added a second nine minutes before the break, Carrasco hustling possession back from Fathi before a cutback from the byline was rifled home by Hazard.
Despite the game fizzling out towards the end, the hosts went on to score a third goal in injury time, a simple tap-in from Marouane Fellaini following great work from Batshuayi.
Belgium face Costa Rica on Monday night in their final friendly before the World Cup, while Egypt's next game is their Group A opener against Uruguay on June 15.
BELGIUM (3-4-2-1): Courtois (Casteels 45'); Alderweireld, Ciman, Vertonghen (Boyata 81'); Meunier (T. Hazard 70'), De Bruyne, Witsel (Fellaini 45'), Carrasco; Mertens (Januzaj 45'), E. Hazard (Batshuayi 45'); Lukaku (Chadli 45')
EGYPT (4-2-3-1): El Hadary (El Shenawy 45'); Fathy (Elmohamady 71'), Gabr, Hegazy, Abdel-Shafi; Elneny, El Said Hamed (Morsy 62'); Warda (Gaber 79'), El Said, Sobhi (Kahraba 67'); Mohsen (Hassan 56')