First-half goals from Michael Keane and Idrissa Gueye proved enough for Ronald Koeman's side, but Hajduk showed enough in the match on Merseyside to suggest that the tie is far from over ahead of next Thursday's second leg in Croatia.
The first opportunity of the game fell to Wayne Rooney, who headed wide of the post after meeting a corner from Kevin Mirallas, while Davy Klaassen also wasted a half-chance as he volleyed over from inside the area.
Everton were setting a high tempo in front of their own supporters, but Hajduk had made a lively start of their own and Nikola Vlasic should have done better when dragging a shot wide of the near post from 14 yards out.
As the first half progressed, Everton began to struggle to carve out any openings against well-drilled opponents but on the half-hour mark, the Toffees went in front when Keane headed home at the back post after meeting Leighton Baines's wonderfully-floated cross.
Moments after the goal, trouble began in the Hajduk section of the stands and after chairs were broken and objects were thrown onto the field, the referee had little option but to order the players to the opposite side of the pitch.
When play resumed, Everton were able to pick up where they left off and in the 45th minute, their lead was doubled through Gueye, who ran onto a neat pass from Rooney before clipping the ball into the bottom corner from 12 yards.
In the fifth minute of added-on time, it should have been three when Rooney received the ball with just Dante Stipica to beat, but the attacker's effort was too predictable and the goalkeeper dived to his left to make a comfortable save.
Soon after the restart, Rooney had another chance to extend Everton's lead but despite meeting Cuco Martina's cross, the summer signing could only head wide of the far post from 10 yards.
However, while Everton held the advantage, Hajduk were arguably the better of the two teams during the second half and the visitors should have pulled a goal back shortly after the hour mark.
Gueye was dispossessed around 50 yards from goal but after the ball was played through to Franck Ohandza, the forward saw his low strike towards the far bottom corner well kept out by Jordan Pickford.
Hamza Barry - who was Hajduk's best player on the night - also had an opening on the edge of the penalty area, but the South African curled the ball marginally wide of the post from 20 yards.
As the match entered the final 10 minutes, Everton were on the back foot and Pickford was required to make two one-handed saves to prevent both Ante Erceg and Hysen Memolla from finding the corner of the net.
Everton rallied towards the end of the game without scoring a third, but Koeman and his players will be more than content with having avoided conceding an away goal to a team who will still fancy their chances of getting back into the tie in front of a hostile crowd next week.