Everton secured their place in Friday’s Europa League draw after further evidence in Croatia on Thursday night that Ronald Koeman’s rebuilding of the team is bearing fruit. If an abracadabra goal from the manager’s latest recruit, Gylfi Sigurdsson, 13 seconds into the second half was the best moment, Jordan Pickford’s penalty save on 65 minutes further deflated Hajduk Split.

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Joan Antoni Carrillo’s team, trailing 2-0 from last week’s first leg at Goodison Park, had brought Stadion Poljud to the boil two minutes before the interval when a thunderous, dipping effort from Josip Radosevic beat Pickford in the Everton goal. The Merseyside club, unbeaten this season, controlled much of the half with another measured, disciplined performance but Radosevic’s effort could easily have unnerved them.

Koeman brought on Aaron Lennon at half-time for his first appearance since he suffered mental health problems in the summer. If that cheered Evertonians and neutrals in equal measure, Sigurdsson’s stunning goal on his full debut went further. The Iceland international, a £45m club record signing from Swansea, closed down a loose ball on the right and as he was falling backwards, sent a looping, angled volley over the goalkeeper Dante Stipica and into the back of the net from 50 yards.

“I saw Gylfi’s goal, but I don’t think everyone on the bench did. It was incredible. I don’t have any other word for it,” Koeman said. “You need to be clever to see that possibility and after two or three weeks of the season, it could be the goal of the season [already]. It was really important to be level so quickly in the second half.”

It meant Split needed three goals, a tall order against a team as well drilled as Everton, who had only conceded once, at Manchester City, before this game.

Yet the hosts should have regained their lead on the night when Ashley Williams conceded a penalty for a clumsy challenge. Ahmed Said won a heated debate about who was going to take it, which did little for an eventual spot kick that was well saved by Pickford. “The penalty save was key as well because there were still 30 minutes to go at that time,” said Koeman.

Everton travel to Chelsea on Sunday and Koeman revealed the Senegal midfelder Idrissa Gueye had been rested with a slight hamstring problem.