After four games, they are level on 10 points with second-placed Chelsea and two behind leaders Manchester City.
"I could have had five," said Lukaku, who was the focal point of almost every attack. "I have to be more (ruthless) if I want to help the team fulfill its objectives."
It looked like it might be another night of frustration for Lukaku as he snatched at a couple of chances but after the break he proved unstoppable, powering home two far-post headers from the right and then the left in the 60th and 68th minutes.
Helping his cause were the pinpoint crosses from Idrissa Gueye and Yannick Bolasie, a constant threat all night, as Everton exploited the full width of the pitch.
The striker scored again in the 71st when he latched on to Kevin Mirallas's through ball to slot the ball past goalkeeper Jordan Pickford with a cool left-foot finish for his third career hat-trick, and second in the Premier League.
MATCH FITNESS
Lukaku put his lack of goals down to a struggle for match fitness following a pre-season heel injury. "I think it was all about fitness levels," he said. "I'm happy for the team."
Everton manager Ronald Koeman thought Lukaku deserved much of the credit for a shrewd tactical switch in replacing England midfielder Ross Barkley with Gerard Deulofeu at halftime.
The Spaniard made an immediate impact in creating attacking width that Sunderland could not deal with.
Koeman has had a huge impact at the club since arriving from Southampton in the close season and the Dutchman is clearly not afraid to make changes if his players fail to produce.
Sunderland manager David Moyes, who spent 11 years at Everton, acknowledged his side gave away soft goals. "When you step up to the big league there are no excuses," he said.
After four games without a win, Sunderland have one point from four games and are facing another relegation fight. "We have to stop conceding goals," said Moyes. "Lukaku is a big threat and we knew that tonight. We needed to pick him up."
(Reporting by Neil Robinson; Editing by Ken Ferris)
