Valencia advanced to the Champions League group stage by holding off Monaco, while Celtic crashed out after losing at Malmo in their playoff-round ties on Tuesday.
Monaco won 2-1 in the home leg but came up one goal short as Valencia went through 4-3 on aggregate.
Former Manchester City striker Alvaro Negredo pounced on an awful Fabinho pass back toward Monaco's goal and chipped keeper Danijel Subasic to provide the opener in the fourth minute.
With Monaco now needing three goals to force extra time, Andrea Raggi got one back in the 17th minute, and Elderson's 75th-minute goal made for a dramatic conclusion, but the Ligue 1 side could not find the last goal they needed.
Spain will be the first country with five teams in a single Champions League group stage, as Valencia join Barcelona, Real Madrid, Atletico Madrid and Europa League holders Sevilla.
In Sweden, Malmo defeated Celtic 2-0 to turn around a first-leg defeat and advance 4-3 on aggregate.
Markus Rosenberg scored the opener for the hosts in the 23rd minute, meaning Celtic needed to find a goal to avoid going out on goal difference.
The Scottish champions thought they had it just before half-time when a corner struck Malmo defender Kari Arnason's hand, which was raised above his head.
The ball fell for Nir Bitton to score, but the officials had already ruled the play dead, thinking the ball had hit a Celtic player's hand.
A Dedryck Boyata own goal early in the second half allowed Malmo to see out a comfortable end to the match.
In other games on Tuesday, Maccabi Tel Aviv held Basel to a 1-1 draw to go through 3-3 on the away goals rule.
Luca Zuffi's 11th-minute goal put Basel 1-0 up on the night and 3-2 on aggregate, but in-form Maccabi skipper Eran Zahavi equalised 13 minutes later and the home side held on to go through.
Zahavi has now scored seven goals in this season's competition, as Maccabi will feature in the group stages for only the second time, and first since the 2004-05 season.
Shakhtar Donetsk overcame a rocky start to qualify, drawing 2-2 with Rapid Vienna for a 3-2 aggregate win.
Playing in the city of Lviv because of conflict in Ukraine, Shakhtar struggled to assert any dominance against a team which had not qualified for the group stage for a decade.
Marlos' 10th-minute opener for Shakhtar was almost immediately cancelled out by Louis Schaub for Rapid, who then took the lead through Steffen Hofmann's free kick.
That goal briefly put Rapid in line to progress on away goals, but Shakhtar responded in the 27th minute when Oleksandr Hladkiy finished off a direct passing move.
Rapid were reduced to 10 men when Mario Sonnleitner received his second yellon 88 minutes, and the Swiss side then missed two good chance to score.
Skenderbeu's hopes of becoming the first Albanian club to reach the group stages came to an end in Zagreb as they were beaten 4-1 on Tuesday despite opponents Dinamo Zagreb playing almost the entire second half with a man less.
Dinamo won the first leg 2-1 and that was the same scoreline 15 minutes into the second leg, with goals from El Arabi Soudani and Armin Hodzic sandwiching an equaliser from Esquerdinha.
Skenderbeu were given a lifeline when Dinamo midfielder Goncalo Santos was sent off three minutes into the second half, but the visitors could not take advantage as the Croatian side added further goals through Jeremy Taravel and Soudani to seal an ultimately comfortable 6-2 aggregate triumph.
The winners will learn their group-stage opponents in a draw on Thursday, while the losing sides will enter the Europa League group stage.