The 23-year-old - who hadn't scored for his club in 13 matches dating back to March - scored all three in the second-half to lift his side into third in the Premier League, two points behind leaders Manchester City.
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.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, the England Under-21 international still reacting brilliantly to tip the thunderbolt header over the bar.
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.
Romelu Lukaku's game by numbers vs. Sunderland:— Squawka Football (@Squawka) September 12, 2016
95% pass acc.
4 shots on target
Hat-trick hero. pic.twitter.com/7OGsW5GL5m