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 draw away to Hajduk Split.
Everton were defending a 2-0 lead from the playoff first leg at Goodison Park, which had been marred by crowd trouble from the travelling supporters, and Sigurdsson's goal provided some needed breathing room as they advanced 3-1 on aggregate.
Josip Radosevic had reduced the Croatian side's deficit with a 30-yard effort just before half-time. 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 Jordan Pickford into the top right corner.
However, the Stadion Poljud was silenced less than a minute after the restart when Sigurdsson, who completed his £45 million move from Swansea last week, looped the ball in with an angled drive from just inside the Hajduk 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.
AC Milan eased into the group stage with a 1-0 win over Shkendija, though the result was in little doubt after they won the first leg 6-0.
Patrick Cutrone, 19, scored his second goal this week in the 13th minute as Milan reached a European group stage for the first time since 2013-14.
Ajax crashed out after Samuel Adegbenro's late brace gave Rosenborg a 3-2 win and turned around a 4-2 aggregate win.
Nicklas Bendtner's first-half goal had put Rosenborg up two goals on aggregate, before Amin Younes and Lasse Schoene scored moments apart in the second half to put Ajax ahead on away goals.
But Adegbenro saved Rosenborg with strikes in the 80th and 89th minutes to ensure Ajax failed to qualify for a European competition for the first time since the 1965-66 season.
Fellow Dutch side Utrecht also failed to advance after Zenit St. Petersburg turned around a first-leg deficit to go through in their place.
Aleksandr Kokorin scored in the ninth minute to level the tie on aggregate, then added a second midway through extra time to win it.
Iker Muniain scored in the first half to supply a 1-0 win and ensure Athletic Bilbao got past Panathinaikos 4-2 on aggregate.
PAOK also went out as Saman Ghoddos' brace for Ostersund put the Swedish side through on away goals, but AEK Athens advanced after securing a 3-0 win over Club Brugge.
Valere Germain scored twice in a 3-0 win as Marseille put away Domzale 4-1 on aggregate after a draw in the first leg.
There will be no European football for Fenerbache this season as they failed to flip the script on Macedonia's Vardar, who won 2-1 in Turkey to advance 4-1 on aggregate.
Among those also going through were Dynamo Kiev, Braga, Maccabi Tel Aviv, Salzburg and Viktoria Plzen. For a full list of scores from Thursday's second legs, click here.
The 22 qualifiers move on to the 48-team group stage, which features the likes of Arsenal, Lazio, Villarreal, Hertha Berlin and Lyon. The draw will be held on Friday. For a look at the seedings and pots, click here.