The 23-year-old -- who hadn’t scored for his club in 13 matches dating back to March -- scored all three in 11 minutes of the second-half to lift his side to third in the Premier League, two points behind leaders Manchester City.
“I think it was all about fitness levels. I’m happy for the team,” Lukaku told Sky Sports. “I think I could have had five in the end. I have to be more of a serial killer for the team to achieve their objective.”
Whilst the victory meant Ronald Koeman became the first Everton manager since Thomas McIntosh in 1919 to win his first two competitive away games, for former Everton handler David Moyes it was sheer misery. His Sunderland side have garnered just a point from the first four matches and have begun a season with four winless games for the sixth consecutive year.
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Lukaku had the best chance of a frenetic first-half where both sides showed a willingness to attack but conjured up few opportunities.
The Belgian frontman, though, might have done better than heading it straight at young Sunderland goalkeeper Jordan Pickford, who reacted brilliantly to tip the thunderbolt header over the bar.
Despite a lot of honest endeavour by the home side, they did little to trouble Everton goalkeeper Maarten Stekelenburg and it was the visitors who ended the half on the front foot.
Koeman made one change at the break taking off an under-performing Ross Barkley and sending on Spanish winger Gerard Deulofeu.
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Sunderland were again on the back foot at the start of the second-half.
They lifted the pressure temporarily when central defender Lamine Kone -- scorer of a brace when the 'Black Cats' trounced Everton 3-0 to ensure they remained in the Premier League in May -- rose above Phil Jagielka but Stekelenburg was equal to the task of saving his 52nd minute header.
Sunderland escaped a minute later when the lively Deulofeu broke free but his whizzing shot was blocked by Jack Rodwell, only for the ball to work its way out to Seamus Coleman.
The Irish international's cross shot sneaked across goal and although Lukaku got an outstretched boot to it it wasn't enough to direct it into the net, the ball trickling wide of the post.
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However, he made no mistake on the hour mark as unmarked he headed Idrissa Gueye's cross past Pickford -- Deulofeu the inspiration behind the goal having won the ball midway in his own half from Wahbi Khazri and bringing it deep into Sunderland territory.
Gueye then went close after Lukaku scuffed his shot before Lukaku saw the crossbar deny him a second in the 63rd minute.
However, he was not to be denied five minutes later as Yannick Bolasie found space down the left, cut to the byline and crossed to an unmarked Lukaku who made no mistake with his header.
Two minutes on and Lukaku raced clear after being found by a superb sleight-rule pass by Kevin Mirallas, and the Belgian striker slotted it nonchalantly past Pickford for his hat-trick.
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