Play was halted for a few minutes in the first half when trouble flared, missiles being thrown and supporters moving towards the pitch shortly after Michael Keane’s 30th-minute header had put the hosts in front.
After stewards and police had moved to bring the situation under control, the players returned to the pitch and Everton doubled their lead in the 45th minute thanks to Idrissa Gueye’s strike.
Aside from the worrying scenes in the stands, Everton will be feeling very satisfied with this how this outing went ahead of next Thursday’s second leg in Croatia.
“I was really happy with the first half and unhappy about the second. We lost a big opportunity to score more goals,” said Koeman last night.
“It’s the fourth clean sheet in a row and that starts with a team’s good defensive organisation and a good goalkeeper.”
The victory was achieved without new record signing Gylfi Sigurdsson, who was not part of the 18 a day on from completing his £45million switch from Swansea but was brought onto the pitch to be introduced to the crowd ahead of kick-off, waving and clapping as he received a warm reception.
The Toffees then made a lively start to the contest, with Ademola Lookman having a shot deflected behind, Wayne Rooney heading wide and Davy Klaassen shooting off-target.
Hajduk made their first real push forward in the 11th minute as Nikola Vlasic struck wide, but Everton were soon back on the attack and Klaassen just failed to make the crucial contact when he slid in to try to get on the end of Lookman’s low ball across the danger zone.
Following further efforts from Rooney and Leighton Baines, Baines burst into the area on the half-hour mark and stood up a lovely cross that Keane headed home at the back post having got above his marker Hysen Memolla, his first Everton goal.
Soon after, Slovakian referee Ivan Kruzliak called the players off the pitch as a melee had broken out in the away section.
With some objects — including pieces of seat, it appeared — being hurled, advertising boards being kicked over and some supporters almost getting on the field, stewards and police swiftly moved over to the area en masse, forming a line around the section.
The situation had calmed down sufficiently by a minute or so later for Kruzliak to allow play to continue, and Everton subsequently extended their lead just prior to the break through Gueye, who took a touch after being fed by Rooney before slotting past Dante Stipica.
Rooney sent a header wide from Martina’s cross early in the second half, before Hajduk fired a warning, Franck Ohandza unleashing a strike that Jordan Pickford pushed away.
Lookman then had a shot blocked by the foot of Stipica, although the flag was up for offside, before Pickford made two smart saves in quick succession, denying substitute Ante Erceg and Memolla.
Meanwhile Swansea City can use the funds generated from Gylfi Sigurdsson’s move to Premier League rivals Everton to sign two or three more players, manager Paul Clement said ahead of tomorrow’s game against Manchester United.
Iceland midfielder Sigurdsson, who played a key part in the Welsh club avoiding relegation last season, completed his move to Everton on Wednesday.
“I spoke to them (chairman and owners) last night about what we will do moving forward. Funds are available to strengthen the squad,” Clement told reporters yesterday.
“It’s a big challenge, no question. We hope we can potentially bring in two or three players to strengthen us in various positions.”
Pickford; Martina, Williams, Keane, Baines; Schneiderlin (Davies 45), Gueye; Mirallas (Besic 76), Klaassen (Calvert-Lewin 62), Lookman; Rooney.
Stipica; Juranovic, Nizic, Carbonieri, Memolla; Gentsoglou (Basic 85), Radosevic, Barry; Vlasic, Ohandza (Said 66), Kozulj (Erceg 66).
Ivan Kruzliak (Slovakia).