Lukaku, 23, has now netted 16 times in the league, one clear of Chelsea's Diego Costa and Alexis Sanchez of Arsenal.
Manchester United's Zlatan Ibrahimovic, Harry Kane of Tottenham Hotspur and Sunderland's evergreen Jermain Defoe, who scored a brace against Crystal Palace on Saturday, sit one further adrift on 14.
The imposing Belgian opened the scoring with a superb curling goal after 30 seconds, bagged a second before the break and added goals three and four in the final 10 minutes of a breathless, thrilling encounter.
The former Chelsea forward was unplayable throughout, combining brute strength with eye-catching skill and subtle touches and provided the assist for James McCarthy's goal in a near-flawless individual performance.
"Romelu showed that he is one of the best finishers in football," Everton boss Ronald Koeman told the BBC.
"Scoring is one of his big qualities. We need to support him, to create. We can improve, but he showed his best today. I'm not surprised because we see it in training."
Lukaku has now scored 59 Premier League goals for Everton -- a tally bettered only by Duncan Ferguson who has 60.
Dutchman Koeman, whose side sit seventh after a run of seven games without defeat, was in shock after one of the most frantic games in Premier League history.
"That's not a normal result," he added "It was a crazy game.
"Both teams changed systems, it was a tactical battle. They made it really difficult for us. We dropped in intensity after half-time, but the reaction to them getting back to 3-2 was good.
"We are getting closer to the top six. We have momentum and we are confident. It's a long way to go until the end of the season. If we keep this up, everything is possible."
(Reporting By Tom Hayward; Editing by Clare Fallon)
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