Valencia ensured Spain became the first country to have five teams in the UEFA Champions League group stage in a single season despite losing 2-1 to Monaco in their play-off round second leg clash.
Nuno's men held a 3-1 lead from the first leg at the Mestalla and gave Monaco - who reached the quarter-finals last season - a mountain climb as Alvaro Negredo opened the scoring with a superb chipped finish in the fourth minute on Tuesday.
Monaco defender Andrea Raggi fired the equaliser into the bottom-right corner 13 minutes later and Uwa Echiejile gave the hosts hope 15 minutes from time, but Valencia held on for a 4-3 aggregate success.
Malmo join Valencia in the group stage, the Swedish side overturning a 3-2 first-leg deficit to progress 4-3 on aggregate with a 2-0 triumph at the Swedbank Stadion.
Captain Markus Rosenberg headed in a 23rd-minute opener for the hosts before Celtic's Nir Bitton had a 42nd-minute controversially had a goal disallowed despite Malmo defender Kari Arnason appearing to handle the ball.
And the tie was settled in the 54th minute when Dedryck Boyata turned into his own net to consign the Scottish champions to a place in the UEFA Europa League.
Maccabi Tel Aviv went through on away goals at the expense of Basel after Eran Zahavi made it 3-3 on aggregate by cancelling out Luca Zuffi's 11th-minute opener for the Swiss side.
Shakhtar Donetsk survived a nervy second leg with Rapid Vienna to progress with a 3-2 aggregate victory after the two teams shared four first-half goals in a 2-2 draw in Lviv.
Forward Oleksandr Gladkiy's 27th-minute leveller proved decisive for the Ukrainian team, with Mario Sonnleitner sent off in the closing stages for the Austrians for a second bookable offence.
Elsewhere Dinamo Zagreb, who had Goncalo Santos sent off, ended Skenderbeu Korce's hopes of reaching the group stage for the first time with a 4-1 (6-2 agg) win.
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