Right, that's all from us. See you at the weekend?
- Play briefly suspended in first half after crowd trouble
- Keane heads his first goal for Everton from Baines cross
- Gueye then slots home from Rooney through ball
- Return leg in Split next Thursday
Everton head over to Croatia next Thursday (20:00 BST), but before then they play Manchester City on Monday night.
City, Croatia, Chelsea on the Sunday. That's a tough week.
A bad night for last year's losing finalists Ajax, who have been beaten at home by Rosenborg.
This image says it all.Copyright: Getty Images
A third goal would have been nice for Everton but a clean sheet was even more valuable.
The Hajduk Split players go over to applaud their noisy visiting fans, who thankfully appeared to behave themselves after that outburst in the first half which led to the game being halted momentarily.Copyright: AFP/Getty Images
Job well done for Everton.
He's back! Mo Besic is in the book for a textbook late challenge on halfway.
Almost job very well done for Everton, as new record signing Gylfi Sigurdsson looks on...
Starting to repay that £30m transfer fee.
Liam Tyrer: Disappointing 2nd half from Everton - sloppy play all over the pitch. Thankfully Pickford is playing well.
Clueless Roberto: Think we should have gone for more goals. Oh and by the way Pickford is a steal at £30 million!
Everton were very good for the first hour but a bit sloppy since. Still, if they come out of the game with a 2-0 lead they will be very happy indeed. Just five minutes or so to keep the ball and don't give any chances away.
Respect from across the city.
DJ Williams: #bbcfootball As a Liverpool fan I tip my hat to Everton. Identified weaknesses and bought fantastically. Liverpool could learn a lot
- Copyright: Reuters
Ooooh that's a chance! Two chances for Hajduk Split as we enter the last 10 minutes. First a cross from the left is almost turned in on goal by Nikola Vlasic, and then Jordan Pickford has to scramble to save a low shot down at his left.
Pickford gives Wayne Rooney a blast, Peter Schmeichel style for giving the ball away cheaply. Hysen Memolla then has a rasping 30-yarder saved by Pickford.
Everton on the ropes a touch. A clean sheet is a must.
Naive from Ademola Lookman as he gives away an unnecessary free-kick in the right-back position, but Jordan Pickford comes to claim it well.
Cuco Martina puts in a cross which Ademola Lookman thumps on target, drawing an excellent save, but the flag is up.Copyright: Getty Images
Don't get too excited, Everton fans
Johnny Magrino: Far too much hype around this performance. Frankly, if Everton do anything other than win tonight, it's a horrendous result.
Joshua Edwards: Toffees fans waxing eloquently, but it's Hajduk Split people - a third tier Croatian team. Get a grip.Copyright: AFP/Getty Images
A first appearance for Everton for Mo Besic since 30 April 2016! He's had some horrible luck with injuries but gets the last 15 minutes in place of Kevin Mirallas.
There aren't many goalkeepers around who can do that. Jordan Pickford claims a catch and in one movement hits a pass on the half volley, maybe 65 yards into the run of Dominic Calvert-Lewin. Sensational distribution.
Rather wild challenge from Hamza Barry catches Ademola Lookman on the thigh, nothing given, and then moments later Barry beats two men and drives a shot wide from 18 yards.
A warning sign for the hosts. They can't get complacent and Wayne Rooney passes on some advice which involves the words 'pass the ball.'
Does anybody want to venture a first-choice Everton XI once the transfer window closes? You'd imagine that Gylfi Sigurdsson will play in behind the striker but where that leaves Wayne Rooney and Davy Klaassen is anyone's guess. Your guess.
Do they still need a number nine? Or is that Sandro's role?
Their midfield has been excellent today.
The Koeman-press. Everton's energy and determination is paying off at the moment.
Benjamin Brute-Moore: The work rate in this side is superb especially in midfield.
Pewak: Hard work gets results - the midfield is full of grafters and neat passers.Copyright: AFP/Getty Images
Midway through the second half, Everton's focus may well switch to keeping a clean sheet now.
A goal there would have made life very different for Everton in next week's second leg. Here's a change as Dominic Calvert-Lewin comes on up front, Davy Klaassen comes off. Wayne Rooney moves back one into the '10' role.Copyright: Reuters