Gylfi Sigurdsson marked his first Everton start with a spectacular goal to help put Ronald Koeman's side into the group stages of the Europa League after a 1-1 away draw with Hajduk Split.
Everton were defending a 2-0 lead from the play-off first leg at Goodison Park, which had been marred by crowd trouble from the travelling supporters, with play stopped during the first half and governing body UEFA launching disciplinary action against both clubs.
Josip Radosevic, though, soon halved the deficit with a 30-yard effort just before half-time.
However, the Stadion Poljud was silenced less than a minute after the restart when Icelander Sigurdsson, who completed his £45million move from Swansea last week, looped the ball in with an angled drive from just inside the Hajduk half.
Jordan Pickford then saved a penalty from Ahmed Said as Everton closed out a 3-1 aggregate win to take their place in Friday's group stage draw.
Wayne Rooney was back in action a day after announcing his retirement from international football with England, but it was the home side who threatened early on.
Forward Ante Erceg was clean through on goal and looked to have been brought down by Pickford, but the goalkeeper was saved by an offside flag.
Erceg then dragged a shot wide after a cross-field pass before Everton finally created an opening after 21 minutes.
Rooney released Cuco Martina down the right and sprinted into the penalty area to meet the return cross, but could only glance his header wide.
Pickford, signed from Sunderland for an initial £25million this summer, produced a fine finger-tip save from Erceg's angled drive, but could not prevent Hajduk from taking the lead after 42 minutes with a fine long-range shot from Radosevic.
The ball was worked back into the middle some 30 yards out, where Radosevic fired in a rising shot, which looked to have taken a deflection off the back of Everton defender Leighton Baines as it flew past Pickford into the top right corner.
The home fans, though, were silenced less than 30 seconds after the restart when Sigurdsson cracked home a memorable strike from just inside the opposition half.
The 27-year-old closed down a loose ball on the right, and as he was falling backwards, sent a looping, angled lob up over the keeper which dropped into the back of the net.
Sigurdsson then almost set up Dominic Calvert-Lewin after breaking clear down the left, but his low cross was cut out at the near post.
After 64 minutes, Ashley Williams conceded a penalty when chopping down Erceg as the Croatian turned into the box.
However, Pickford produced a fine stop down to his right to push out Said's spot-kick.
Erceg almost got clear after a defensive mix-up, but was eventually closed out.
Rooney broke clear late on, although the former England captain could not produce the needed finish as his shot was beaten away by the keeper.