Everton 2 - Hajduk Split 0: Michael Keane and Idrissa Gueye put Toffees in control

But manager Ronald Koeman was unhappy with a second half showing which almost saw his side let their advantage slip.

The trouble, which saw the visiting support throwing objects including seats following the opening goal, will be reviewed by UEFA after it caused a four-minute stoppage to the first leg meeting.

Everton have already warned supporters travelling to the away second leg next week to be especially vigilant about the prospect of trouble from home hooligans.

But on the evidence of last night, Koeman’s side should have enough to deal with whatever the Croatians can throw at them on the field.

Koeman said: “I think we missed a big opportunity to score more goals and decide qualification.

“If you’re 2-0 up at half-time in a Premier League game, you know it’s three points. But this is two games and with a better result the second leg would be even easier. Now it will be difficult.

“We were 2-0 up at half-time and there was a chance for Wayne to score the third but then we dropped the tempo in the second half.

“We had a fourth clean sheet in a row which is always nice but maybe Jordan Pickford was the one player on the pitch who played at a high level for 90 minutes.”

The tie was marred somewhat by crowd disturbance shortly after Keane had given Everton the lead, involving a large number of the 1,500 fans who had made the journey from Croatia.

Supporters surged forward and were involved in altercations with stewards as both sets of players moved to the opposite side of the field and play was held up for two minutes.

Sadly, the unrest between those supporters and the stewards continued sporadically and saw police drafted in as support.

And it was a distraction that Koeman could have done without although he must have been pleased with the first half performance at least.

The opening goal came at the end of a half-hour of near-complete domination from Koeman’s side and also at the perfect time, just as a trace of frustration was beginning to creep into Goodison.

It was created, and scored, by two England defenders - convenient with Gareth Southgate in the stand - as Leighton Baines showed great tenacity in winning a loose ball following a corner before surging past a defender to the left-hand by-line.

There, the full-back sent over the perfect, hanging cross which allowed Keane to climb above marker Hysen Memolia and head in his first goal for the club since joining from Burnley for £30 million this summer.

The crucial second came on the stroke of half-time as Everton showed they had put the off-field distractions firmly behind them.

Davy Klaassen created it with a strong challenge in midfield and pass to Wayne Rooney which found the former England captain at his most effective, slipping in a perfect through ball which Idrissa Gueye converted coolly from 10 yards.

Rooney, forced into action as an orthodox striker in place of the injured Sandro, threatened with an early header just wide as young forward Ademola Lookman looked particularly threatening.

But the veteran striker could not add to his first goal of the season at the weekend, and missed a great chance on the stroke of half-time when clean through, hitting the keeper.

Instead, it was the Croatians who looked more likely to claim a third goal even though it was not until the 61st minute that Pickford was called into action, diving to keep out Franck Ohandza’s shot.

Nikola Vlasic miskicked from six yards, Ante Erceg’s shot was turned around the post by Pickford and the Everton number one made an even better stop from Memolla’s stinging, long-range attempt.