After seeing his first-half header brilliantly saved by Jordan Pickford, the Belgian was in devastating form scoring twice with his head, before coolly slotting home in a stunning second-half period to move Ronald Koeman's side to third in the Premier League table.
Chances for both sides in goalless first-half
Everton travelled to Sunderland just 124 days after the two sides last met at the Stadium of Light and Sunderland's 3-0 win on that occasion was a defining result for both teams. Sunderland secured their top-flight status, while the curtain fell on the reign of Roberto Martinez at Goodison Park. Martinez's predecessor made just one change to the side that beat Stoke City before the international break, with fit-again Seamus Coleman replacing Mason Holgate at right-back.
Sunderland, and former Everton manager, David Moyes, made two changes as he looked for his first win since taking over at the Stadium of Light. Jan Kirchhoff returned in place of former Blue Steven Pienaar, while Duncan Watmore started up front in place of the injured Fabio Borini.
Both managers saw their sides have good opportunities to open the scoring in an open and end-to-end start to the match. Jermain Defoe showed great movement and anticipation to reach a shot that was deflected behind the Everton defence and into his path. However, the striker, who is normally so sharp in front of goal, lifted his shot over the crossbar from eight yards out.
Everton had a great chance to take the lead, moments later, after a superb cross from Yannick Bolasie was met by the head of Romelu Lukaku on the edge of the six-yard box. The Belgian's wait for a goal continued after Jordan Pickford produced a brilliant save to divert Lukaku's header over the crossbar.
Lukaku's header was the last clear sight of goal in the half as the Blues dominated possession but lacked purpose and concentration going forward against a well-drilled and organised Sunderland defence. Papy Djilobodji was a real barrier in the Black Cat's resolute defence and the Senegal international produced a good block to deny Kevin Mirallas' goalbound effort after good play by Bolasie.
Maarten Stekelenburg reacted well to tip over Lyndon Gooch's cross, which looked like it might have crept into the top corner, before Bolasie unleashed a venomous shot over the crossbar from the corner of the Sunderland penalty area.
Lukaku completes second-half hat-trick
Ronald Koeman looked to Gerard Deulofeu to inspire his side's attack in the second-half as the Spaniard replaced Ross Barkley at half-time. Barkley didn't appear his usual self in the first-half, conceding possession 11 times. Deulofeu took his position on the opposite flank to Bolasie and the latter forced Pickford into a diving save at full stretch with a good effort from the left corner of the box.
Lamine Kone, who scored two goals when the two sides last met in May, headed for goal from a corner but it was collected by Stekelenburg. At the other end, Seamus Coleman's powerful drive across goal was turned just wide of the far post by Lukaku.
The Belgian didn't have to wait much longer for his elusive goal as he ended his goal drought in the 58th minute. Idrissa Gueye's cross was inch-perfect for Lukaku to head past Pickford to score his first Premier League goal since March. The Everton pair joined up again, but this time Gueye fired narrowly over the crossbar after good work from Lukaku.
Lukaku came close to scoring his second of the game just after the hour-mark. The striker turned his man inside the penalty area before striking against the crossbar with Pickford beaten. With the score still at 1-0, Sunderland remained a threat and Everton captain, Phil Jagielka was well-placed to block Duncan Watmore's effort to end Sunderland's counter-attack.
The Everton striker then doubled the Toffees' lead, heading home Bolasie's cross from the left for his second goal of the match and to leave David Moyes' side with work to do with just over 20 minutes to play. If Sunderland did not have a mountain to climb after Lukaku's second goal, they did soon after as the Belgian completed an 11-minute hat-trick.
Lukaku coolly slotted home his third goal of the match after being released by a lovely through ball from Mirallas to complete what is the 12th quickest hat-trick in Premier League history. The Blues continued to dominate possession in the closing stages to extend their unbeaten start to the season and move to third in the table.