Klaus-Jan Huntelaar scored four goals including two penalties as Schalke blasted back from a two-goal first-leg deficit to hammer HJK 6-1 and reach the Europa League group stage.
The Bundesliga side had been left reeling by last week's loss in Helsinki but it took Huntelaar 15 minutes to reduce the deficit from the spot and despite Teemu Pukki's equaliser on the night, he added his second after 25 minutes.
The second half was all Schalke as Huntelaar twice, Kyriakos Papadopoulos and Julian Draxler added further goals against their shell-shocked visitors to ease through 6-3 on aggregate.
Atletico Madrid left wantaway striker Diego Forlan at home but it made little difference as they eased to a 4-0 win at Vitoria for a 6-0 aggregate win, with Adrian scoring twice.
Premier League Fulham went through 3-1 on aggregate despite a 1-0 defeat to Dnipro in Ukraine, while PSV Eindhoven shrugged off last week's goalless draw in Austria by thumping Ried 5-0 at home.
Last year's losing finalists Braga scraped through on away goals after a 2-2 draw with Young Boys of Switzerland. Former European champions Red Star Belgrade were thumped 4-0 in France by Rennes for a 6-1 aggregate loss.
Poland'sLegia Warsaw staged a stunning comeback to beat Spartak Moscow 3-2 in the Russian capital for a 5-4 aggregate win. Legia trailed 2-0 on the night but capped their recovery with Janusz Gol's injury time winner.
On a dismal night for Scottish football, Rangers went out 3-2 on aggregate to Maribor after a 1-1 home draw, and Celtic, down to 10 men after the second minute dismissal of Daniel Majstorovic, lost 3-1 on the night and on aggregate to Sion.
Two early goals from Joseph Akpala saw Club Brugge to a 2-0 win over Zestafoni and 5-3 aggregate success, while Belgian rivals Anderlecht edged through 4-3 on aggregate after a 2-2 draw with Bursaspor.
In a stunning upset in the Stadio Olimpico, Peter Stepanovsky scored in the 82nd minute to give Slovan Bratislava a 1-1 draw on the night with Roma and a 2-1 aggregate win.
Simone Perrotta had cancelled out Slovan's slim first-leg advantage with an 11th minute effort, but the home side failed to build on that lead and Stepanovsky's strike embarrassed the Serie A giants.
There were no such problems for Roma's city rivals Lazio, who wrapped up a 3-1 win over Rabotnicki in Macedonia for a 9-1 aggregate victory, with Tommaso Rocchi scoring twice.
Tottenham eased through 5-0 on aggregate after a goalless home draw with Hearts, while Premier League rivals Stoke and Championship side Birmingham also progressed with easy home wins over Thun and Nacional respectively.
Shamrock Rovers became the first Irish side to reach the group stages of a European competition as Stephen O'Donnell's extra-time penalty gave them a famous 3-2 aggregate win over Partizan Belgrade.
Sevilla were knocked out after a 1-1 home draw with Bundesliga side Hannover. Mohammed Abdellaoue gave the German side the lead and an Emanuel Pogatetz own goal was not enough for the Spaniards, who went out 3-2 on aggregate.
French Ligue One side Sochaux were stunned 4-0 at home by Metalist after last week's goalless draw in Ukraine, but Paris St Germain wrapped up a 6-0 aggregate win over Differdange of Luxembourg with a 2-0 home stroll.
Dutch side AZ overturned last week's 2-1 reversal to Norway's Aalesund in style, winning 6-0 in Alkmaar. Martin Hinteregger's strike was not enough for Salzburg, who went out on away goals to Omonia Nicosia despite a 1-0 win on the night.
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