Lukaku marked the occasion with a brace before half time as the Toffees raced into a 3-0 lead against Newcastle United before eventually running out 3-2 winners at Goodison Park.
The Belgian striker, who is currently on loan from Chelsea, had been behind Nikica Jelavic in the Everton pecking order earlier in the season and is happy to have finally made his Goodison bow.
"I loved it, I have waited to make my home debut for a long time. My team-mates really helped me and from minute one I was focused," BBC Sport quotes Lukaku as saying.
The result means that Everton remain unbeaten this season and also lifts them up to fourth in the Premier League table.