Lukaku is a world-class striker and he is still improving

score four goals to win games.” It took Lukaku just 30 seconds to get off the mark, equalling Chelsea’s Pedro for the fastest Premier League goal this season.

And things quickly became a lot worse for the Dorset daydreamers, who found themselves trailing 3-0 within 30 minutes.

Morgan Schneiderlin almost immediately set Everton on the attack.

And when James McCarthy swept the ball in to Lukaku, the big Belgian turned and curled a finish around Artur Boruc.

Koeman had started with £ 11million teenager Ademola Lookman for the first time. The 19-year-old rewarded him with a performance brimming with confidence, Koeman claiming: “He will be a great player.”

There was no stopping Lukaku, who displayed the menace that saw some of Europe’s top clubs covet the former Chelsea striker.

He burst into the box and his cut back was forced over the line by McCarthy at the second attempt, the unfortunate Simon Francis unluckily assisting his opponent’s cause. If Francis was able to curse the gods for Everton’s second, there was only one person culpable for the third.

Inexplicably, the Bournemouth skipper – under no pressure – passed straight to Lukaku, who was lurking in the penalty area.

He gleefully notched his 14th league goal of the campaign.

Francis was hooked at halftime along with ex-Evertonian Dan Gosling. Goals No.15 and 16 followed for Lukaku – but only after Josh King pulled back two goals in quick succession which jangled the nerves of home fans.

But a stupendous Lukaku volley seven minutes from time made it 4-2 and a clever Ross Barkley backheel sent him through for his fourth goal.

Harry Arter got another for Bournemouth before Barkley sealed Everton’s victory.

Howe said: “I wouldn’t be doing my job properly if I wasn’t concerned. It wasn’t pretty, was it? It is very difficult when you come here and defend like that.

“The first goal killed our preparations.”